The Reds ended a six-game losing streak - and 13-match winless run – in the Championship as Domingos Quina’s second-half goal moved them five points from safety.
Asbaghi also celebrated his first league win in charge at the thirteenth attempt – the longest wait in the club’s history.
“Of course you feel good after a victory,” he said.
“I think for us as well, with the results we have had this season, this win comes at a really good moment.
“It was a win that I felt was well deserved. I think we played well.
“In the first half, maybe we were a little too open and they were allowed to have too much on the ball.
“I felt that coming into the second half, we adjusted that pretty well. We were much more aggressive in our pressing in the second half.
“When I watched the second half, I honestly felt that we were the better team. It was a great goal from Dom that puts us in the lead and you never know how we’re going to react, defending a lead because we haven’t done that so much.
“I felt that the players did it in a mature way. It gives a lot for the confidence, I hope.
“The only way you can unite everybody in and around the club is to win football games and play good.”
Barnsley return to action away to Coventry City on Saturday.