Manager Roberto Mancini has set his side the target of winning three of their last four games to claim a Champions League slot, with Saturday's encounter at the Emirates Stadium appearing to be the most demanding.
Although it is the first time Mancini has led his charges into combat with Arsene Wenger's men, for City as a whole it is another trip to opponents they have not beaten on enemy territory since 1975.
Arsenal's recent move means City's record at the Emirates is not that bad in comparison to their hapless return at Highbury.
But it is something that needs to change if the Blues are not to concede an advantage to Tottenham, and let both Aston Villa and Liverpool back into the battle for fourth.
However, Richards, who is set to return from a knee injury, does not believe his team-mates have any need to feel inferior.
With two wins against Arsene Wenger's men under their belts already this term, the England international is in bullish mood.
"We have beaten them twice already this season, so why not again?" said Richards. "Arsenal will want revenge and they are a different team at home.
"At the Emirates they probably play the best football in Premier League but we can beat anyone on our day. As long as we are right, nothing else matters."
While most of the talk surrounding the game has focused on Emmanuel Adebayor's return to his former club for the first time since his £25million move, Kolo Toure has been the former Gunner who has been lifting spirits around Eastlands this week.
Toure and resident joker Shaun Wright-Phillips have tried to ensure the mood was not too downbeat after City's last-gasp derby defeat to Manchester United which, combined with Tottenham's shock win over Chelsea, saw Harry Redknapp's men leapfrog back into the top four.
"Kolo tries to lift the mood and then Shaun gets everyone going," said Richards. "I still believe we are looking healthy.
"The games coming up are hard but we tend to play better against the better teams, Our aim is the top four, which is realistic and we have to work hard for it."
It would be easy to label defeat this weekend as catastrophic for City's Champions League hopes, but Mancini does not quite see it that way.
With Aston Villa to face next Saturday and then a potential winner-takes-all clash with Spurs to come on May 5 - both at Eastlands - before the final game of the season at West Ham, there is enough opportunity to make up lost ground.
Clearly though, the margin for error is slim.
"Liverpool and Aston Villa are very close now," Mancini said. "But we have four games to play, they have three each. There is a difference, and also Aston Villa meet us at home.
"We still have a good chance. We can afford to lose one from here to the end. It is important to remember that."