Fans regularly chanted for the sacked Italian throughout their disappointing 3-2 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."
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- Premier League