England, who finished on 210 for nine in their second innings after a tense final session, had their backs to wall from the time Sri Lanka skipper Hashan Tillakaratne won the toss.
"It was an outstanding Test match and the character we showed after losing the toss was tremendous," Vaughan told reporters.
"To come out of Galle (with a draw) having lost the toss was a fantastic result and an outstanding effort considering that last time we played here (in 2001) we were hammered."
Vaughan added that England knew the last day would be extremely difficult batting on a wearing pitch against off spinner Muttiah Muralitharan, who finished with match figures of 11 for 93.
"We always came into the final day trying to be positive but, with Murali around, you know it can go bang, bang, bang pretty quickly," he said.
"The way they nullified him today was a very good effort. The longer the day went, you could see them (Sri Lanka) panicking more."
Vaughan reserved special praise for the efforts of Test debutant Paul Collingwood, who batted three hours for his 36, and Ashley Giles, who took a career best with the ball and then batted for 111 minutes to help save the game.
HUGE KEY
"Paul Collingwood was a huge key for us getting this draw," he said. "He showed a tremendous amount of guts and I think he has a hell of a future in Test cricket.
"For him (Giles) to make the technical change (with his bowling) in Bangladesh was a big decision but we backed him and he came up with the goods here."
Sri Lanka captain Tillakaratne refused to be downcast about the result, claiming his side would be encouraged by their dominance of the match.
"Yes, it was disappointing but there were so many positives in this test match to take with us to Kandy," he said. "We played some brilliant cricket.
"We held the advantage in this game and morale remains very high," he added.
Muralitharan, the man of the match, was philosophical despite a frustrating afternoon full of turned down appeals.
"These things happen," he said after claiming his 12th 10-wicket haul in 83 matches. "We put up a really good effort but well done in the end to England, they played really well to survive.
"The wicket got slower and slower and, although it was hard to play shots, it was quite easy to defend in the end."
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