Barry was forced to apologise last season after he and other teammates allegedly stole a taxi in Barcelona, leading them to being booed by fans upon returning to the pitch.
However, Moore has stood by his players and urged fans to do the same as the Baggies aim to improve their performances after being relegated from the Premier League last season.
"Gareth is a very intelligent player, somebody that understands the game, and the different challenges," he said in a pre-match press conference. "He's one that can spot danger. He's effective with the ball at feet, his work in and out of possession is excellent.
"I hope there was no real animosity towards him anyway. Gareth Barry is a tremendous player, we're delighted to have him at the club.
"He's worked hard in pre-season, and for somebody of Gareth's age to affect games the way he does, his fitness is good. He'll play a big part."
Moore's side will face Stoke City at The Hawthorns in their Championship clash on Saturday.