These two men, who through the Heysel Stadium disaster were destined to become great friends, hardly saw each other as the events unfolded. Robinson, then secretary, now chief executive of Liverpool Football Club, was with his fellow officials, or talking to the press, or moving about the stadium trying to find out what had happened. Barettini, who as the right-hand man to Giampiero Boniperti, then the Juventus president, liaised between his club and their opponents, remained with his Italian colleagues.
"I didn't have much contact with the Italians," Robinson recalls. "But I do remember standing on the touchline and seeing Giovanni Trapattoni, the Juventus coach, across the pitch. He saw me, and began to walk towards me. He had to come some distance and when he reached me he just shook me by the hand and said, 'I'm terribly sorry, Mr Robinson.' "
Barettini's encounter came later, about an hour and a half after the match had ended. "In front of the stadium was a big concourse, by now totally empty except for police at one end, and two buses - the Liverpool bus and the Juventus bus. I was on my way to our bus and as I walked across the concourse I saw a man coming towards me from the Liverpool bus. He came up to me and just said, 'I am very sorry for what has happened,' and then he turned and went back. It was Bruce Grobbelaar. This is something you cannot forget."
These mirror-image gestures pretty accurately reflect the state of mutual sympathy that has existed between the two clubs in the decade that has passed since the death of 38 Juventus supporters just before the start of the 1985 European Cup final marked the blackest chapter in the history of European football.
In an atmosphere surprisingly free of recrimination, at least at official level, bonds were forged between Liverpool and Juventus of a kind that only apply in such circumstances. A shared tragedy brought the clubs together, and they responded accordingly.
On the first anniversary of Heysel, a group of Liverpool supporters and officials joined hundreds of Italians at a memorial service in Turin. Visitors from Turin found a special welcome for them at Anfield. The transfer of Ian Rush from Liverpool to Juventus in 1987 arose in part out of these new-found links. And there was a sense in which not just the clubs but the cities themselves were joined. For example, the Liverpool and Turin fire services organised football matches against each other, with the teams granted the use of Anfield.
The two clubs have never played each other since Heysel, although they were close to organising a friendly in South Africa last summer. It is something Robinson would like to see happen before the day comes when they are drawn once again to meet in European competition.
That will be a poignant moment. In the meantime, it seems, the relationship between the two clubs has weakened. This is partly because of personnel changes - not so much at Liverpool, where Robinson and the manager Roy Evans provide a connection with the past at the highest level, but at Juventus, where the presidency of Boniperti has given way to that of Roberto Bettega, and a new era has been ushered in.
For Juventus, the anguish of what happened when hundreds of fans rampaged across Z block, adjacent to the Liverpool end, and a wall collapsed under the weight of fleeing Italians has always been tempered by the fact that few of those killed came from Turin. They were people from all parts of Italy who happened to be living in Brussels at the time. In buying tickets there, they unwittingly by-passed crowd control procedures which, in theory, should have ensured that this section of the ground remained neutral.
The focal point of the tragedy was thus blurred. Turin as a community could not share in the loss in the way that Liverpool did after Hillsborough. And on the 10th anniversary of Heysel, which falls tomorrow, little officially is happening. Who is anyone, outside Liverpool and Juventus, to say it should? But in taking his lead from Juventus, Robinson would have liked Liverpool to play its part in any commemorative event. As it is, the club is marking the occasion by commissioning a new memorial plaque, to add to the one discreetly sited in the Liverpool offices, which will be on display in a re-housed, expanded club museum underneath the Kop. Liverpool plan to invite Juventus to its unveiling when the new museum opens next year.
But on a personal, individual level, Heysel, like any tragedy of such proportions, shaped and continues to shape the lives of many people. Peter Robinson and Franco Barettini, for example, two of those most closely involved with picking up the pieces.
Robinson, now aged 59, is one of the most experienced and respected administrators in English football. He became the Liverpool secretary in 1965, having learnt the ropes at Stockport, Crewe and Scunthorpe. Tall and paternalistic, he is acknowledged for his courtesy and calmness; indeed, you cannot separate him from the exemplary way the club has conducted itself going back to the Shankly era of which Robinson became a part.
Barettini is 65, retired now from his work with Juventus, which, with his skills as a linguist, put him close to the seat of power. He still lives in Turin, where he began his career in business. For Robinson, Barettini combines what he sees as the very Italian traits of excitability and sophistication.
The two knew each other a little before Heysel. In January, 1985, Liverpool and Juventus met in the Super Cup as, respectively, European champions and Cup-winners' Cup holders. The match was supposed to have been played over two legs, but their schedules were crowded and they agreed to make it a one-off affair. "I think the relationship was struck up over a very small thing," Robinson recalls. "When we decided we could only play one game, we tossed up to decide the venue with an English coin. Franco thought that was extremely funny."
Barettini was quickly enamoured of all things Liverpool. He speaks now of the efforts that were made to clear the Turin airport runway of snow when they flew in to play in the Super Cup - as if this effort might not have been made for other clubs.
In the weeks leading up to Heysel there was almost daily contact between the clubs. "From day one I was concerned about this neutral area," Robinson says. "I argued all along that we should have one end and Juventus the other. There were so many stories emanating about black-market tickets. We suggested there should be a meeting between the two clubs, but the Belgian authorities said no.
"As late as the Monday of the match I arranged for a fax to be sent to Uefa and the Belgian Football Association, but nothing was ever done. It wasn't even acknowledged. There were serious planning mistakes. That doesn't excuse what happened, but the problems would not have occurred if it had been done in a different way."
The day itself began with an exchange of gifts between delegations of which Robinson and Barettini were members. Then, the long evening, "the terrible decision about whether to play the match or not" (Barettini) and "the pandemonium of people wanting answers you couldn't give them" (Robinson).
At such times, as Barettini says, friendships are made. "Peter is such a nice, kind person it was practically impossible not to be friends. He was like a brother." In the aftermath of it all, the two men and their families became frequent guests in each other's homes. There were invitations to Wembley and Anfield and wet days out in the Lake District. Barettini's daughters came to Liverpool to further their studies, and in Turin Robinson was honoured with the role of walking one of them to the church door on her wedding day before her father gave her away.
They still talk about Heysel - "about how it could all have been avoided", Robinson says. That is a constant theme in the aftermath of any disaster, and for the bereaved of Heysel it will return tomorrow, and for many more days and years to come.