Striker Barnes missed seven matches through suspension after tripping referee Nigel Miller at Bolton last month.
But he made a triumphant comeback with two goals as Brighton cemented their place in the top six with a 6-1 thrashing of Blackpool on Saturday.
"I'm pleased for him because I know him and I know how much it hurt him being out for so long," said Poyet.
"I know how difficult it was to cope with seven games away and I know how much we missed him. He helps us with goals and by working hard to give us another option while defending.
"It was a great day to have him back because Leo (Ulloa) was very tired after Peterborough. Having Ash fresh and desperate to play made it the perfect game for us to use him.
"The first two weeks out were very difficult for him but recently he's been so good in training and everything was going in for him, it was incredible, and that gave me the chance to give Leo a rest.
"His first touch was perfect, he made great decisions and he scored two goals. Everything went right for him and it's like having a new player for the rest of the season."