Fans regularly chanted for the sacked Italian throughout their disappointing 3-2 Barclays Premier League loss to Norwich at the Etihad Stadium.
With City having failed to retain the title they won last season, or impress in Europe, Mancini was relieved of his duties on Monday with Kidd taking caretaker charge.
As after Tuesday's game at Reading, assistant manager Kidd did not attend a post-match press conference but did speak to television reporters.
Kidd, who also paid tribute to Mancini in his programme notes, told BBC Sport: "It's been an emotional week with the events at the club.
"Full credit to the lads, they've got stuck in and given their best and you can't ask for any more.
"I understand the cheers for the boss, he would have been disappointed if there wasn't for what he did here."
Kidd will remain in charge for next week's tour of the United States, which will see them play friendlies against Chelsea in St Louis and New York.
He said: "I've been blessed and been grateful for what football has given me.
"I was asked to take charge for two games and America, which has been tough with the boss going.
"The club make the decisions and you abide by it. I'm a big boy.
"We have fallen short of the standards we set last season, but it hasn't been for a lack of effort.
"You defend as a team and attack as a team, so you have to look collectively, but we haven't reached that consistency."
Norwich struck through Anthony Pilkington, Grant Holt and Jonny Howson and were good value for their victory despite two excellent equalisers for Jack Rodwell.
The victory lifted the Canaries into 11th place in the table and a satisfactory finish after almost getting dragged into the relegation fight.
Manager Chris Hughton said: "I'm absolutely delighted with that.
"It shows, irrespective of the anxiety at certain periods, it is really about where you finish at the end of the season.
"We are delighted to have done that.
"We had a very good spell before Christmas, where we were excellent. We found it difficult after Christmas to get the wins we needed and the formulas but we have finished the season strong.
"It would have been nice to be a bit more consistent right the way through but I am delighted to have finished where we have done.
"Even up until a couple of months ago, when we were having a difficult spell, most people couldn't see us finishing in 11th place but that is the league.
"It is about getting the results when you can and hitting good form when you can."
Hughton felt the hosts were in good spirits and provided a stern test despite the emotionally draining events of the past week.
Mancini's sacking came just two days after a dismal loss to Wigan in the FA Cup final.
Hughton said: "They certainly didn't look vulnerable at Reading in midweek, with the goals they scored and the opportunities they had.
"They are a team that is full of quality players. On most occasions, you come out on the worst side of that, because of what they have got.
"They showed that at Carrow Road, we were 2-0 down after five minutes.
"I think it was an end-of-season game where you have got 22 players on the park that desperately wanted to win.
"You are always going to have to defend well against the quality they have got and sometimes you need a bit of fortune along the way but overall I thought the performance was excellent."
Hughton added that player of the season Sebastien Bassong missed the match as a precautionary measure and would have played had more been at stake.
He also suggested Pilkington, who was withdrawn nine minutes from time, could be doubtful for the Republic of Ireland's upcoming friendlies and World Cup qualifier against the Faroe Islands.
Hughton said: "He has to rest - he has a tendon injury that has hampered him a little bit of his season.
"We have to make sure we make the right decisions as regards him.
"He has come strong at the end of the season but it is certainly an injury he has to rest."
When asked if it might limit his international duty, with Ireland also due to play England, Georgia and Spain, Hughton said: "We will see, we will be in conversations with them."
There were reports City left-back Aleksandar Kolarov was involved in an angry exchange with supporters during the game but club officials were unable to comment.