Villa host the runaway Premier League leaders a week today in a match pushed back due to their opponents involvement in the FA Cup semi-finals this weekend.
Relentless City have won 27 of their last 29 matches in all competitions but did see their momentum checked by a shock 2-1 defeat at home to Leeds on Saturday.
Smith claims that should give Villa heart as they look to bounce back from a 2-1 defeat at Liverpool.
He said: “Leeds have gone there and beat them (City) with only two shots on goal. It just shows you how crazy football can be. We have a great belief in our team.
“Our performance in the last 20 minutes against Fulham and on Saturday was better. But we can’t be so loose on the ball as we were in the first half-an-hour at Anfield.”
The loss to the Reds was Villa’s fourth defeat in eight matches.