Barry made 440 appearances for Villa in 11 years before making the £12 million switch to Eastlands during the summer with just one year remaining of his contract. But the England midfielder was booed from the minute he stepped off the team coach until the final whistle by sections of Villa supporters as City fought back to earn a 1-1 draw.
Given said: "I was a little bit surprised by the reaction to Gareth. He deserves a lot of credit for what he has done for Villa."
He continued: "It is a bit harsh on him getting booed and the reception he got.
"He was at Villa for so many years and did great service, got them £12 million after Villa hardly paid a penny for him as well, so I thought it was a bit unfair.
"It was a bit strange. I suppose some fans think one thing and others think something else. But Gareth has come to us and wants to further his career and hopefully win trophies and I think the fans should respect what he has done for the club and move on.
"I am sure there will be a majority of Villa fans who will be thankful as well for the service he gave to the club but the majority at the game were pretty much the opposite."
Given added: "Fans up and down the country are perhaps a bit jealous of Man City in the sense that they have new owners and what they can bring to the club.
"But they should respect Gareth for what he did beforehand."