They did not get that precious away goal but they will still be relatively confident of overhauling Lamberto Zauli's 16th-minute goal for Vicenza at Stamford Bridge in a fortnight's time.
But not that confident. Had it not been for Ed De Goey, Chelsea's Dutch goalkeeper, Vicenza would have secured a victory large enough to make the second-leg of this semi-final an academic exercise. For an hour the Italians were everything Vialli had suggested - and more. Not only were they organised and hard-working they were also slick and imaginative.
"We made a few mistakes and paid heavily," Vialli said. "But I am not going to criticise my players because we all worked our socks off. They will now come to Stamford Bridge knowing they can counter-attack which is how they want to play against us.
"But to go through we will have to be perfect, which is hard when you are 1-0 down. We were not perfect tonight but I am confident we can turn it around. Ed De Goey played very well. We are still in the game because of him."
Chelsea did improve in the later stages but, De Goey apart, their fans were the only visitors to emerge with credit. Having been sacked by the barbarians in 899 the city of Vicenza, with its World Heritage-listed Palladian architecture, had taken no chances of a repeat. Alcohol was banned all day and enough police were on duty to perform a man-marking role on the 1,200 Chelsea fans.
When they arrived they were greeted by driving rain (three sides of the ground were without cover) and a pamphlet newspaper demanding "English go home''. It was not a provocative reference to the evening's visitors but to Vicenza's parsimonious and unpopular English owners, a London investment company.
Vicenza were at full strength for what they had billed as the most important match in their 96-year history but Chelsea were without Sunday's hero, Frank Sinclair. All their Azzurri played with Vialli leading the attack and Gianfranco Zola and Dan Petrescu supporting from the midfield flanks. That, at least, appeared to be the theory. In practice the plan was a failure and it was not until the anonymous Petrescu was withdrawn that Chelsea gained parity of performance.
They had started brightly with Zola bringing Pierluigi Brivio into action from 20 yards but Vicenza quickly responded and, after 13 minutes, almost scored. Zauli met Gabriele Ambrosetti's corner powerfully at the near post, but De Goey brilliantly clawed the ball away with his left hand.
It proved a brief respite as, four minutes later, Fabio Viviani, on the left, chipped a ball into Zauli whose movement and control wrong-footed Michael Duberry, Franck Leboeuf and Eddie Newton before he rolled a left- foot shot past De Goey.
The goal dispelled any feelings of inferiority Vicenza may have had and they now seized control. Had they scored a second, after 25 minutes when only brave blocks by Leboeuf and Duberry denied Domenico Di Carlo and Viviani, it would have been deserved.
Chelsea, looking tired in mind and body after Sunday's Coca-Cola Cup exploits, hung on to half-time but suffered bookings for Leboeuf and Roberto Di Matteo soon afterwards. The first, for dissent, was stupid but the second was more damaging: Di Matteo will miss the second leg. The Spanish referee, who was excellent, also booked three Vicenza players but all will be available in a fortnight.
Chelsea's passing and decision-making was still indifferent and Leboeuf almost cost his team a goal when he was caught in possession well upfield. The ball was moved quickly to Ambrosetti whose cross was headed wide by Pasquale Luiso. A minute later the striker went much closer, bringing another fine save from De Goey after a slick one-two with Zauli.
Somehow Chelsea were still only one down but, as they still showed little sign of scoring themselves, Graham Rix finally made a change just before the hour. Off came Petrescu, who appeared to aim a few choice words at the coach before disappearing down the tunnel, and on came Tore Andre Flo. Within minutes Zola hit the outside of the post, possibly unintentionally, from a tight angle on the right. Three minutes later Vialli, leading by example, rose to meet Zola's corner only for Ambrosetti to kick his header off the line.
Vicenza remained more threatening and only another fine save by De Goey, from a far-post cross, enabled Chelsea to head back to England with optimism.
Chelsea (4-5-1): De Goey; Clarke, Duberry, Leboeuf, Le Saux; Petrescu (Flo, 61), Wise, Di Matteo, Newton, Zola (Morris, 87); Vialli. Substitutes not used: Hitchcock (gk), M Hughes, Granville, Nicholls, Myers.
Vicenza (4-4-1-1): Brivio; Mendez, Belotti, Dicara, Viviani; Schenardi (Beghetto, 72), Di Carlo, Ambrosini, Ambrosetti (Stovini, 72); Zauli (Firmani, 86); Luiso. Substitutes not used: Falcioni (gk), Coco, Baronio, Di Napoli.
Referee: M Diaz Vega (Spain).