Sergio Aguero's goal earned City their first ever Champions League group stage victory on Tuesday night, and Barry believes that they will go to Old Trafford with a spring in their step.
"A last-minute goal can lift everyone - it is a massive confidence booster," said the England midfielder.
"We will just go into Sunday's game, knowing it is a massive one, with a little bit more confidence."
However, Barry is also aware of the task facing his side as they take on the Premier League champions.
"But it is not a place you can go and relax - we have got to go and play our best game of the season to get something out of it," he added.
"We respect Manchester United and hopefully it will be a good game."
The Blues go into Sunday's clash two points ahead of Manchester United in the Premier League table.