The Italian was relieved of his managerial duties at the Etihad Stadium on Monday, a year to the day after guiding City to their first Premier League title, leaving Kidd to take charge of Tuesday's clash against the Royals.
That three-point haul clinched a second-place finish for the recently dethroned champions and Kidd was delighted at the professionalism of the players as well as praising the support of his staff behind the scenes.
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"Everyone - the staff, the fans and the players - did it for the club tonight, so I'm pleased. It was special effort from the players and the backroom staff have been terrific as well - the support from them has been really good."
Kidd admits he was shocked at City's decision to sack Mancini but revealed his relief that he was able to get the club back on a winning front after the disappointment of losing to Wigan in the FA Cup final compounded a sub-standard campaign.
"I would have just taken the result tonight," he added. "If you had said to me you are going to get three points and clinch second place, I'd have accepted that - the way the last 48 hours have gone. We aren't greedy and we don't have to qualify now, we're second.
"All credit to the players, they are the ones that have had to put up with stuff off the pitch as well. I'm pleased for them because it would have been a travesty if they hadn't finished second.
"It's not me, I've just come in and been asked to take the team for two games. As a Manchester lad, I couldn't say no."