Saints' strike pair James Beattie and Kevin Phillips (2) scored all three goals to leaved City rooted near the Premiership table drop zone.
"You can smell the fear," Sturrock said after the impressive 3-1 win at The City of Manchester Stadium.
"Their home form has not been what it should be and with the quality of players they have Manchester City should be in a different part of the league to the one they are in now.
"That makes people nervous. Decision-making becomes difficult and the supporters got on their backs which doesn't help confidence.
"As an opposition team, you have to play on that and overall I am very pleased with the performance."