Kevin Pietersen cracked 101 for his 10th Test hundred that ensured England saw the fifth day out safely on 369 for six after being set a world record victory target of 500.
India were jubilant after stumps were drawn, not because they had failed to win the match but because they had managed their first Test series win in England for 21 years, emulating Kapil Dev's team in 1986.
"I think it's a fair result," Dravid told reporters. "England dominated the first Test match and we dominated the next two.
"We played the better cricket at the critical moments and to come away from home and beat England, who have been traditionally so strong for the last six or seven years, gives us a lot of satisfaction."
Vaughan still sounded frustrated by the first Test result at Lord's when rain prevented England from taking the 20th Indian wicket for a 1-0 lead but accepted India had finished on top.
"We did everything we could to win that game (Lord's) and there's not a lot you can do when the weather intervenes.
"But in the last two matches, India have put us under a lot of pressure and usually over a three-match series the team that plays the best cricket comes out on top. India have just pipped that because of the way they played in the last two games."
NO FOLLOW-ON
Dravid said he felt "very proud" of the achievement, adding that it meant more because it was only India's third series victory in England since 1932.
The India skipper still received some criticism from observers who felt he should have enforced the follow-on at The Oval on Sunday instead of batting again. Some pundits believe that decision cost India the chance to win the series 2-0.
"There will be different opinions on what was wise and what is not wise," Dravid said.
"But as captain of the team I know my players and the dressing room pretty well, I know the workload that my bowlers have had after playing all series.
"I know people might be disappointed that we didn't enforce the follow-on and maybe if I was sitting in a living room I would have thought the same but as captain I get a pulse for what is happening and I did what I thought was right."
Vaughan defended Dravid on the decision and said he would have made the same choice.
"They were 1-0 up and wanted to make sure they won the series," Vaughan said. "I would have done the same."
