The Midlanders currently occupy the final relegation spot in the Premier League standings, but three points against Roberto Mancini's men would help them leapfrog Wigan.
And with crucial games against fellow strugglers Reading and QPR to come, Lambert feels Villa have shown enough quality in recent weeks to compete against the champions.
He said: "I felt there were signs of encouragement against Arsenal but then I've felt that for a few weeks without getting the results.
"That's the frustrating thing, when you play well and don't get results especially the games at Everton, West Brom and Swansea.
"When you have a two-goal lead at Everton and West Brom and you don't see it through, or concede a late equaliser as was the case at Swansea, it's frustrating.
"If you had taken maximum points from those games, then you'd be sitting mid-table and, against Arsenal, we should have had at least a point."
Lambert added: "People are asking about the Reading and QPR games and I say to them, 'so there's no point in playing Manchester City then?'
"I don't view it that way. We may as well just give it to them if we think like that. We want to beat Manchester City.
"You are there to win, regardless of whether it is City or QPR or whoever. We have to try and win. We are a threat going forward. We are not going into it just to draw or anything like that.
"There are 33 points available still and that's a hell of a lot of points to play for.
"I've said before it's going to be one hell of a ride to the end of the season, that's for sure. Never a dull moment, never is."