Kevin Pietersen smashed 53 off 39 balls as England finally found success on their Indian tour with a six-wicket victory in the lone Twenty20 international in Kolkata on Saturday.
The tourists enhanced their reputation as the reigning world Twenty20 champions by keeping the hosts down to 120-9 before surpassing the modest target with eight balls to spare.
Pietersen, who was dropped on one by Suresh Raina, led England's charge with three sixes and four boundaries.
Samit Patel helped Pietersen add 60 for the third wicket after two wickets had fallen by the seventh over with the score at 40.
"It's been a very tough month for us," said Swann.
"We played some abjectly horrible cricket on the tour, but it came together today. However, one swallow does not make a summer. We need to improve."
Pietersen, who was named the man of the match, conceded the dropped catch helped his cause.
"It was a tricky wicket," he said. "It was one of those wickets where you had to take a risk in the first six overs. Luckily I was dropped."
Speaking about the tour, Pietersen said: "India is a good place to come and play as a batsman, but a lot of us under-performed. But believe me, we tried our hardest.
"We've got a lot of work to do technique-wise here in the sub-continent. We've tried really hard on this trip, although we came unstuck in the one-dayers."
Dhoni, who will get a few days off before the Test series against the West Indies starts on November 6, said his team had only fallen 15 runs short of a decent total.
"It was the sort of wicket where you would aim for around 150 runs," he said. "It was very difficult to score runs. It will be good to take the next few days off before we go to the Tests."
Earlier, Raina top-scored in India's innings with 39 off 29 balls, including two sixes and four boundaries, while Dhoni made 21 before being run out off the final delivery.
The ninth-wicket pair of Dhoni and Ravichandran Ashwin (17 not out) boosted the total by taking 25 runs from the last two overs.
It soon became 26-3 as Alex Hales took a brilliant running catch on the deep mid-wicket fence to remove Virat Kohli for 15 off Bresnan.
Manoj Tiwary settled in with Raina to help India reach 65-3 in 10 overs, before he was bowled by Patel for 15.
Finn struck twice in two balls, having Raina caught at point before bowling Ravindra Jadeja first ball, to reduce India to 74-6 in 12 overs.
Source: AFP Global Edition