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 said 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," the left-hander said ahead of tomorrow's second ODI. "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 home criticism in recent weeks, with a Test series defeat to England and a 2-1 reverse against Pakistan fuelling the discontent.
And while Gambhir did not buy into Cook's assessment, he was also keen not to appear downbeat about the home side's prospects.
"We're a team who has done very well in one-day cricket as well. We're the No 3 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."
Cook, meanwhile, is content to be leading a relatively fresh-faced England side in India this month after accepting the need for rotation in international cricket.
The England and Wales Cricket Board has long pursued a policy of resting the players with the heaviest schedules and, with a Champions Trophy, back-to-back Ashes contests and a pair of series against New Zealand all coming up in the next year, that shows no signs of abating.
The batsman Jonathan Trott, the opening bowler James Anderson and the first-choice spinner Graeme Swann have all been excused the five-match series.
"Careers are short but rest and rotation is going to be an important part of the side moving forward," Cook said.
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