Balotelli, who made his first start in six matches at the DW Stadium on Wednesday, endured a largely frustrating night but remained focused and gave City the lead with a 69th-minute strike.
James Milner added the second three minutes later with a stunning effort to seal the 2-0 win for Roberto Mancini's side.
"Any striker's first league goal is going to be massive in a season. To be fair to Mario, he has not had loads of chances," Barry said.
"When you do get them you need to score them. He has taken a chance with his start here. It could be good for Mario. Hopefully he can go on a run now.
"Mario is not going to lack in confidence if he misses two or three. He'll keep trying the same things. Hopefully his goal will give him a bit more confidence and he can improve from there."