Hughes was ditched by the club's owners and board as they believed City's Champions League qualification campaign had stalled.
"The race for fourth is not done yet," said Mancini. "Wednesday is a final. It will probably be City's most important game in 10 years. We must beat Spurs.
"We must concentrate like we did against Aston Villa," added the Italian. "It is important we put on a performance. If the Villa match was a semi-final, then Wednesday is a final."
Tottenham beat Bolton 1-0 on Saturday to retain their slender point advantage over City, who came from a goal down to defeat Aston Villa 3-1 and end their hopes of qualifying for the Champions League.
Redknapp sets sights on Man City
Spurs can get away with a draw at Eastlands in midweek, provided they win away at relegated Burnley on the final day of the season, to keep hold of their first top-four finish in 20 years. City's last game of the seaon is away at West Ham.
"The City game is absolutely massive," said Spurs boss Harry Redknapp referring to Wesnesday's match. "City are a terrific side, in good form, and we must go there, in front of a bumper crowd, and try to get something out of it.
"But this is what playing at this level is all about. As a manager, and as players, you want to be involved in big games - and this is one of those, no doubt."
What is clear, however, is that the race for fourth is now a three-horse race, with Liverpool - who host Chelsea on Sunday - just about still in with a chance but Villa out of it.
O'Neill rues two-minutes of madness
Villa's defeat at Eastlands means the highest they can finish is fifth.
"It has been a fantastic effort by the team all year and we took the fight to the second last game of the season," said Villa manager Martin O'Neill.
"We have more points than last season, when we had 62 and finished sixth. Teams are getting stronger and we are competing with sides who have very good players.
"It has been a great season and I do not accept that we have come up short. We reached the carling Cup final and the semi-final of the FA Cup.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.