"Not inspired enough," he added dolefully. Scotland's hard-earned reputation for winning more friends than matches of consequence is a burden that threatens to stay with them well into the first Hogmanays of the next century.
McAllister is not alone in believing that the Scots will forever be the brave fallers at the first hurdle of major competitions unless they stop believing that you get medals for insignificant victories and, above all, start scoring goals on important occasions. Easier said than done for a country that used to be the production line for England's top division but has been replaced by cheap imports from eastern Europe.
Like Scotland's delightfully unpretentious coach, Craig Brown, McAllister deplored the notion that going out in the first round would not have mattered if they had beaten England. Even so they admitted that if they could fail to find the net when the incentive was as great as it was at Wembley, there was not much hope.
Too much was left to McAllister, who modestly thought he failed. He said David Seaman's save from his penalty was a "devastating turning point". Added to that, he thought anxiety became overwhelming at Villa Park once they realised that they had to score a second goal.
They had celebrated the first, scored by Ally McCoist after two blatant misses, as if they had won the trophy itself. McAllister said: "We should have been concentrating on getting straight back at them." He confessed that he got "quite emotional". After all, before the finals began, McCoist was the only member of the squad to have scored more than 10 goals. That, said Brown, revealed all too much about Scotland's real chances.
Too much was expected of McAllister and McCoist, who roomed together at the team's hotel. Neither had slept much after the match against England. "It just kept going over and over in my mind," McAllister said. "I knew that if I had to take another one I would: I wanted to make up." The Swiss made sure they never put a foot out of place to let him have a second chance.
While several of the Scottish players gained by the experience - especially John Collins, for whom, amazingly, no Premiership club made a serious bid last season - the man with the most enhanced reputation was Brown himself. Before he was appointed a survey of fans revealed that only eight per cent thought he should be given the job. "I was surprised that many had heard of me," he said.
Brown says that qualifying for the next World Cup is going to require "some changes - some freshening up". He entered Euro 96 with more than half his squad over 30 and an average age of 29. "The spirit was so good that everyone, young and old, felt they wanted the first World Cup match to be tomorrow."
In fact it will be in August against Austria, and in two years time, when the finals are held in France, several of the team will be on the verge of retirement. The hope in Scotland is that Everton's Duncan Ferguson will eventually come to the rescue as a striker. In a way the situation is similar to England relying on their own wayward wizard, Paul Gascoigne.
McAllister himself is 31 and said that Euro 96 was, for him, the "big one". The question is whether Brown has the raw material with which to produce a new side capable of remaining as determined as any in the world but with a cutting edge.
Bearing in mind that some Scottish national teams of the past had much more individual talent than the one he must soon rebuild yet they still failed to get past the early rounds of either the World Cup or European Championship, the omens are not good. Brown, however, said: "We went home early again but I think everyone recognises that this time we played differently, more composed. We have to make changes, but we have something good to build on."