Kidd saw his side win 2-0 at relegated Reading but said after the victory that the sacking of his former boss came as a surprise to him.
Manuel Pellegrini remains overwhelming favourite to become Manchester City manager following the sacking of Roberto Mancini - a move that came as a surprise to players and staff.
The Italian saw his three-and-a-half-year reign at the Etihad Stadium brought to an abrupt end on Monday - a year to the day after bringing City their first league title in 44 years.
It was also announced that assistant manager David Platt, who was offered the chance to stay on, had decided to join Mancini in leaving.
Failure to retain the Barclays Premier League crown and a poor showing in the Champions League pushed Mancini towards the exit door, with Saturday's surprise FA Cup final defeat to Wigan proving the final straw.
Malaga coach Pellegrini is favourite to replace the former Inter Milan boss, having been heavily linked with City since rumours of Mancini's demise began to surface.
Despite such reports, the sacking came as a shock to his assistant Brian Kidd, who oversaw a 2-0 win at relegated Reading on Tuesday night.
"What has gone on in the last 24 hours was a shock to the staff, and before the game I would have just taken the result, to get the three points and take second place," he said.
"It's all credit to the players - they are the ones who have had to put up with stuff off the pitch. I am pleased for them because it would have been a travesty if we hadn't finished second.
"I was asked to take charge for two games, and, being a Manchester lad, I couldn't say no. I wouldn't have been able to walk down Market Street if I had.
"You'd have to ask the players how they feel. We appreciate the fans, and they were disappointed, and we were disappointed, on Saturday. What you've seen is a combination of a couple of things, but I think it was a relief because it has been a tough 48 hours."
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- Roberto Mancini
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