Now the former Celtic boss wants the 2010 squad to take the first step towards such glory in Sunday's Carling Cup final clash with Manchester United at Wembley.
O'Neill said: "Winning a trophy is the ultimate. There is no getting away from that and it would be fantastic.
"We have a lot of pictures of the old teams around the training ground and why not? It is something to aspire to.
"I have often said to keep the pictures up on the walls of the 1981 league-winning side and 1982 European Cup-winning side. The early 1980s was a fantastic spell for Villa.
"The history of the club is there to see, a great tradition, so we'd like to try and do something about it. That is really what the team is there for."
O'Neill believes lifting silverware for the first time for the current crop of players will have major significance in their development.
He said: "Winning the first trophy is the most difficult. I remember way back, when I was a player at Nottingham Forest, we won the Anglo-Scottish Cup.
"We played Ayr and Kilmarnock in the early rounds and Leyton Orient in the final and we won it and the manager, Brian Clough, was in raptures about it because it was the first trophy we had won.
"He felt himself it was the start of something. The trophies the team won in the next couple of years, the league title and the European Cups, were founded on winning that trophy. That was very important.
"In the big scheme of things no-one would pay any attention to it - but it was important to win that first trophy."
O'Neill appears to have a virtual clean bill of health with skipper Stiliyan Petrov winning his battle to overcome a virus which kept him out of the FA Cup fifth-round replay win over Crystal Palace in midweek.
Brad Friedel, James Collins and Emile Heskey, who were all rested for that game, will come back into contention to be part of the starting line-up at Wembley.
Friedel is likely to be preferred in goal to Brad Guzan even though he has played all five matches in the Carling Cup so far this season.
O'Neill, who was upset by criticism of his team's tactics by Arsenal manager Arsene Wenger earlier this season, was irritated by the Frenchman's dismissal of the Carling Cup following the same match, a 0-0 league draw at Villa Park last month.
Wenger said: "If you win the League Cup, can you honestly say you have won a trophy?"
O'Neill, who has won the trophy twice as a manager with Leicester in 1997 and 2000, claimed the Frenchman took the competition seriously when it suited him.
Quoted in several national newspapers, he said: "I know that the Arsenal manager has been pretty scathing all the time about the League Cup.
"I would have said that the team he played against Wigan (in the semi-final second leg in the 2005-06 season) was very strong.
"So when it suits, it's a great competition. When it doesn't suit, it's not.
"If you had seen or experienced either of the two semi-final matches between Manchester City and United, if somebody had told those clubs that this trophy wasn't a trophy, then I think you would have been given short shrift."
Man. Utd 5/6, Draw 12/5, Aston Villa 7/2