The forward was suspended for seven matches after deliberately tripping referee Nigel Miller in their clash with Bolton Wanderers last month.
The 23-year-old returned to the fold with two goals in the club's 6-1 win over Blackpool at the weekend.
"I'm pleased for him because I know him and I know how much it hurt him being out for so long. 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," Poyet told reporters at a press conference.
"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."
Brighton currently sit fourth in the Championship table.