Asbaghi’s side were holding their own in the first half, despite being a goal down to Danny McNamara’s opener and had opportunities to score themselves.
However, Barnsley conceded a second almost immediately after the restart – again through McNamara – and despite pulling one back soon after through Romal Palmer, the visitors shippin another two with Oliver Burke and Benik Afobe on the scoresheet.
Asbaghi was pleased with how his relegation-threatened team performed in the opening period but criticised his players for what they displayed after the break.
He said: “I think in the beginning of the first half we looked better than a team that was fighting for the play-offs.
“But if you look at the overall performance in the 90 minutes, it was not good enough for a team that wants to stay in the league.”
Barnsley now face an almost insurmountable task to stay in the second tier of English football.
They need to claw back Paul Ince’s Reading – who sit eight points clear of the Tykes – with just six games remaining and have a difficult challenge on Easter Friday when they travel to in-form Swansea.
“We let the fans down, and they were the best Barnsley players today by far,” added Asbaghi.
“We have to make sure that they cannot see that in the next game we play against Swansea.
“We will put on a bigger fight. It is going to be even tougher. It is going to be against the most comfortable team on the ball in the league.
“We have to make sure that next time they travel to watch us they will see players that will go in with their heads first in every duel, unlike today.”