India lost the fifth and final Test at the Oval by an innings and 244 runs, succumbing in less than three days.
"I remember saying, when we were 1-0 down, that I still thought we were going to win the series. I had a lot of confidence in the talent and amount of skill we had in the dressing-room. I didn't think we'd win quite so emphatically, as we have done," said Cook after the match.
"Southampton was clearly a turning point for us, to finally get the win. Suddenly after that first day (there), there was a bit of confidence back in us as a side. Once we won there, and enjoyed that night, that was the route of how we wanted to play our cricket against these guys," he added.
India have been consistently under pressure from James Anderson and Stuart Broad throughout the series, and it didnt help that they lost wickets regularly to their second line of attack in Chris Jordan, Chris Woakes and Moeen Ali as well.
"We have to give credit to the five bowlers for the way they've bowled because with sustained periods of pressure, we haven't let them get away from us. That's very hard to bat against" said Cook.
"They didn't get more than 150 in four innings, and all our batters scored runs, so it's almost like the perfect games. It's tough cricket and it tests you in different conditions.
"They're very fine players. They've had a very tough series against a very good bowling attack. Like we all do, they'll look at their games and see where they can improve in these conditions. They've got fine records as cricketers, so there's no reason why they won't bounce back," the skipper said.