Dhoni himself was guilty of gifting away his wicket when he chased a wide delivery from Ben Stokes and handed an easy catch to Steven Finn.
India were all out for 253 in a chase of 275.
"We gave away too many wickets, quite a lot of soft dismissals, and because of that we were not able to chase the runs. Shikhar, Ambati, myself, we should not have lost those wickets, in the last ten overs we can get those runs but we lost soft dismissals," Dhoni said at the post-match presentation.
"We need to improve our slog, the last ten overs with the bowling, Shami has done a good job but other fast bowlers need to step up. We don't want to concede so many we can't chase them down," he said.
The Indian skipper said keeping everyone fit was the "most difficult thing " on this tour.
"England tour has been 77 days, then we go to Australia before the World Cup, so it will be important to stay fresh.