Scotland failed to reach the finals in England the following year, yet Smith still believes his team can make a bigger splash. They lie second from bottom in Group Five, but even after facing the Italians this evening in what he called "our biggest test", their remaining games are against their three rivals for the runner's-up spot, with Wednesday's tussle with Norway in Oslo a potential six-pointer.
Although Scotland are outsiders, Smith's first four matches in charge have encouraged optimism among their supporters, if only because he has restored morale and organisation to a squad who were drifting badly under Berti Vogts. Today's contest at Hampden is a 50,000 sell-out, with Scots snapping up tickets returned by Italy and a feelgood factor palpable in the players' pre-match pronouncements.
Temperamentally, Smith is closer to the canny, calculating Craig Brown than to the Braveheart bluster of Ally MacLeod. Far from hyping up Scotland's chances of finally doubling their number of wins over Italy, he injected a note of realism.
"None of us - players, staff or myself - are miracle workers," said the former Rangers and Everton manager. "Six months ago, people were calling us the worst team in Scotland's history. Now they can't suddenly expect this to be one of the best ever. That can't happen, but they are making progress.
"They are certainly more confident than they were. It wasn't so much a fear of representing Scotland as a sense of despondency that had to be lifted. We've had a good response in terms of determination and the defensive aspects of the game, and we're now better placed to acquit ourselves well in a game of this standing."
Scotland scarcely embarrassed themselves in the first meeting with Italy in March - his first game - when it took two exquisitely curled free-kicks by Andrea Pirlo to defeat them in Milan. Smith suggested that they were arguably the better side in the second half, but he wants a sustained improvement rather than spirited cameos.
"If we are going to make progress - to do anything in the World Cup or European Championship - we have to achieve decent results against one of the leading nations. We have to challenge the top-seeded sides - and do it consistently, rather than beating the Netherlands 1-0 and losing the return match 6-0 like we did two years ago."
To that end, Smith has put in place "structure", the initial aim of which is to make Scotland hard to beat. The fact that they have not conceded a goal during open play in his three competitive fixtures is a sign that the demands he has made in terms of work-rate have produced the required response. The next step is to make them a greater attacking threat, and he is confident that uniting Barry Ferguson, Darren Fletcher and Nigel Quashie in midfield for the first time will enhance their creativity.
Two of that trio are Champions' League regulars and are therefore unlikely to be fazed by the household names and stellar reputations of Marcello Lippi's Italy. Smith is a self-confessed admirer of the Italian game and of Lippi in particular. "Anyone who can win five Serie A championships as well as the European Cup has to be a top man," he said. "But it's not just what he has won, it's the way he goes about his football."
The former Juventus coach has done more than most to change perceptions of his country's football. In 1965, when Smith saw Greig take Jim Baxter's pass and bludgeon an 88th-minute winner, it was renowned for its emphasis on regimented and brutal defence. Now he expects Lippi to play the three forwards he started with in the 2-1 victory over the Republic of Ireland in last month's Dublin friendly, namely Christian Vieri, Alberto Gilardino and Alessandro Del Piero, whose inclusion would probably mean a substitute's role for Francesco Totti.
Italy are far from invincible. Knocked out of the last World Cup finals by South Korea, they lost to Wales en route to Euro 2004 and failed to advance beyond the group stage in Portugal. The current campaign has produced a 1-0 loss in Slovenia and a scrappy 4-3 home win over Belarus. A revitalised Scotland are capable of inflicting further discomfort, although the pragmatist in Smith will realise that success in Norway, while raising fewer eyebrows, might well prove of greater value.Reuse content