Kidd was put in charge for City's final two games of the Premier League season and next week's tour of the United States after Mancini was sacked last Monday.
Mancini, who took charge in December 2009, won the FA Cup in 2011 and topped that by winning the title last year.
There has been little comment from the club since the statement announcing Mancini's departure but Kidd, in the programme notes for the last league match against Norwich, has acknowledged his contribution.
Kidd said: "Naturally, the events of last week have been widely reported and debated.
"Roberto and his team have achieved so much here and have provided trophies and some of the most memorable moments this club and the supporters have ever seen.
"I know all at the club and all of you, the fans, are grateful for the success that he and his team helped to bring about and we all wish him the very best for what will no doubt continue to be a successful career.
"Now, however, it's important that we look forward both to this game and towards an exciting summer and new season ahead."
There was a further pictorial tribute to the departed manager in the programme with images of the defining moments of his reign under the header 'The Mancini Years'.
A caption read: "Thank you to Roberto Mancini and his team from all at Manchester City Football Club."
Former City manager Kevin Keegan had earlier expressed his surprise at the timing of Mancini's sacking.
Keegan, who managed City between 2001 and 2005, admitted the club had failed to build on the success of winning the Premier League but said that was not entirely Mancini's fault.
A year to the day that City won a thrilling final day game against QPR to pip rivals Manchester United to the title, Mancini was told his services were no longer required.
Keegan said: "(It's) surprising if you look at the length of time, but if you look at what's happening in football now (it's) not surprising at all.
"It was a season where they (the club and the manager) didn't build on the last season. They didn't make any progress and, in fact, they took a step backwards."
Keegan felt City should have gone on to more success after Mancini added the Premier League title to the FA Cup and Community Shield.
"They made a mistake in that they didn't strengthen the side in the right way having won something. The signings this season have been poor and that's what cost them."
Keegan felt claims that falling out with City's players had cost Mancini his job were a convenient excuse for the club's owners.
He added: "They (the club's owners) are looking at reasons to justify sacking someone who 365 days earlier had won something for them. They couldn't turn round and say he hasn't done a good job, three trophies in three seasons after they hadn't won anything for so long was fantastic."
Keegan believes Mancini's successor - with Malaga coach Manuel Pellegrini the favourite - will be expected to deliver silverware.
"I think he will realise he's going to a club that has ambition. He's going to a club that already has a lot of good players," he said.