City overcame United 2-1 at Old Trafford to narrow the gap at the top to 12 points and Barry was pleased with the performance, although he knows it will probably not make a difference in the title race.
He said: "To win at Old Trafford two years in a row sets a good standard for our club.
"The players were desperate to get three points and we would have been disappointed to get anything else, even a draw.
"To win for a second year running is a fantastic feeling, but there is some frustration that we haven't played like that more often.
"Even before the game kicked off, our players were thinking that we wished there was a little bit more at stake and the gap was a little bit closer."