City came from behind - courtesy of Sergio Aguero's late winner - to defeat Villarreal 2-1 to keep their hopes of qualifying for the knockout stage alive and Barry says the way the victory came about has given them plenty of self-belief ahead of the huge derby with Manchester United on Sunday.
"A last-minute goal can lift everyone - it is a massive confidence booster," said Barry.
"We will just go into Sunday's game, knowing it is a massive one, with a little bit more confidence.
"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.
"We respect Manchester United and hopefully it will be a good game."