It has been a difficult past week for the deposed champions of last season with dismal defeat to Wigan in the FA Cup final followed by the sacking of manager Roberto Mancini.
Richards felt the players showed their spirit by winning comfortably at Reading in their penultimate game of the campaign on Tuesday.
The 2-0 victory at the Madejski Stadium, which came less than 24 hours after confirmation of Mancini's departure, was enough to secure second place in the Barclays Premier League.
Richards, who stood in as captain in the absence of the rested Vincent Kompany, told the club's website, www.mcfc.co.uk: "The game at Reading was massive for us because we'd just lost to Wigan and we needed a win and a good performance and we delivered on both counts.
"Reading may have already been relegated but we played really well and would have beaten most teams with that display."
Richards feels the team will now have the freedom to entertain in their final Premier League game against Norwich at the Etihad Stadium on Sunday.
Mancini's former assistant boss Brian Kidd remains in interim charge of the team.
Richards said: "There's no pressure on either us or Norwich so I think you'll see an open, entertaining game and hopefully that will reflect in our play."
City's season does not end on Sunday as the squad fly to the United States the following day for a week-long post-season tour which features friendlies against Chelsea in St Louis and New York.
Kidd has been asked to remain in charge of team affairs until the end of that trip.
The veteran coach, a former City and Manchester United player, could then remain at the club to provide some continuity into the next regime.
Six other members of the backroom staff, including first-team coach David Platt and reserve-team boss Attilio Lombardo, left the club after Mancini.
Malaga's Chilean Manuel Pellegrini is the firm favourite to succeed Mancini, who won the FA Cup in 2011 as well as the Premier League last year.
City have not commented and Malaga do not want the issue to overshadow their remaining fixtures in the Primera Liga, which conclude on June 1.
For Richards, a change of manager could offer him the chance to re-establish himself in the City side after a season ruined by injury and, at times, appearing to fall out of favour with Mancini.
The 24-year-old has missed most of the campaign with knee and ankle injuries and has watched as Pablo Zabaleta has not only secured the right-back spot, but arguably been the club's player of the season.
Zabaleta's sending off in the FA Cup final allowed Richards to return at Reading but he actually played most of the game at centre-back after Kolo Toure went off injured.
Richards said: "I enjoyed playing at centre-back at Reading and I always have done so it's always nice to get a chance to play there.
"I've played alongside Joleon (Lescott), Vincent and Kolo over the years and it feels very natural for me when I play there and if and when I'm needed, I know I can do a good job for the team.
"The last six months have been really hard but I'm just happy to be back now.
"The fans gave me a great reception against West Brom and they appreciate I'll always give 100 per cent whenever I play and though this season is almost over, I'll be in good shape and ready to go for the start of next season."
Striker Sergio Aguero was also forced off injured on Tuesday and was being assessed along with Kolo Toure ahead of the Norwich clash.
Kompany and Matija Nastasic will be back in contention after being rested by Kidd in midweek.
Richards believes Kidd could opt to make more changes as the season reaches its conclusion.
He said: "I don't know what the team is going to be yet or who will play, but maybe it's a chance to see one or two of our younger players against Norwich.
"I've played for the EDS (elite development squad) a couple of times this season and know there's some really good talent coming through so I hope they get the chance to show what they can do."