Former England poacher also praised Sir Alex Ferguson's Manchester United despite their 3-1 defeat but insisted they had no chance of stopping the Catalan giants at Wembley
Barca completely outplayed Sir Alex Ferguson's side at Wembley, with goals from Pedro, Lionel Messi and David Villa enough to secure a comfortable victory for the Spanish champions.
Many believe that the result cemented Pep Guardiola's side as the greatest ever but Lineker feels that the current side must become European champions at least two more times if they are to emulate the greatest teams in history.
Writing in his News of the World column, he said: "Other teams have played wonderful football but when you add fitness and mental strength, you have a side that are well on the way to becoming the greatest club side of all time.
"To achieve that status, Pep Guardiola's team will have to win the Champions League two or three more times.
"However pretty your football, your legacy is ultimately judged on silverware. The early Real Madrid teams and Arrigo Sacchi's AC Milan lifted the trophy as well as raising the bar in terms of what football could be.
"You would not bet against this Barcelona team doing it. Only Carles Puyol is nearing the end of his career and they did not really miss him last night, did they?"
United had looked to get back into the game through Wayne Rooney's equaliser less than 10 minutes after Pedro broke the deadlock, and Lineker praised the Premier League champions for attempting to play their own game.
He said: "Wayne Rooney's goal came out of nothing but you have to give United credit. They approached the game in the right way.
"It is not in their nature to destroy, to play the sort of anti-football which allowed Real Madrid to win the Copa del Rey and spoil the semi-final. In those two games, Real did their best to bring Barca down to their level. We saw some of the theatrics which are probably Barcelona's only flaw.
"But United brought out the best in them. Even after the equaliser, there was only one team in it.
"The smile which Sir Alex Ferguson gave Guardiola at the end said it all: When Barcelona play like that, you really have no chance."
Lineker also lauded the game as a spectacle, insisting that it will have been good for football's image in the global sporting arena.
He said: "This was what football needed. At a time when the game is being dragged through the gutter again by events off the pitch, by allegations of FIFA corruption, by money, by agents, this was the antidote."