City fell behind to Demba Ba, Cesar Azpilicueta and Oscar goals despite dominating the first half but Javi Garcia began the fightback, Edin Dzeko struck twice and Micah Richards grabbed a late winner.
Kidd, in charge following Roberto Mancini's dismissal earlier this month, said: "I thought we were unlucky to go in 2-0 down but the players were tremendous.
"They have had a tough couple of weeks after losing the manager and the FA Cup final.
"It has been a draining, emotional couple of weeks.
"They have done great work in New York with the appearances and events for the club, they have done great work.
"We only had one training session, so that might be the secret. You can't say enough about them."