The tourists came to India with a dismal recent record in 50-over cricket in the country, losing consecutive series 5-0 in 2008 and 2011 and not winning a single fixture since 2006.
But that streak was halted in the series opener in Rajkot, where England secured a nine-run win on a high-scoring pitch.
Cook insisted afterwards that the home side should still be expected to claim the series in conditions that have proved so profitable in the past, but Gambhir was unmoved by the claim.
“I think there are no favourites when two good teams play against each other,” said the left-hander ahead of today’s second ODI in Kochi.
“There are no underdogs either. Whoever does the best on that particular day will end up winning the match, like England did last time.
“There are no favourites. I think he is just trying to underplay (England’s chances in) the series. England are a good side and whoever plays better will win the series.”
India have come under some strong local criticism in recent weeks, with a Test series defeat to England and a 2-1 reverse in a three-game rubber with Pakistan fuelling the discontent.
And while Gambhir did not buy into Cook’s assessment of the odds, he was also keen not to appear downbeat about the home side’s prospects.
“England have done well but we can’t forget last time they were here they lost 5-0,” he said.
“We don’t need to look at what England are doing, it’s about what we want to do out there.
“We’re a team who has done very well in one-day cricket as well. We’re the number three side in the world and we need to look at the areas where we have strength and minimise the weaknesses.
“It is a new start, a new game. Rather than take what happened last game we want to go out there as if it was a four-match series rather than think we are 1-0 down.”