Following the game, Asbaghi spoke to the club's media about The Reds' start to the game, Barnsley's chance creation, resilience from The Tykes, keeping a clean sheet and Barnsley's home form.
On Barnsley's start to the game
"I think we started this game really well, pushing them down and creating a lot of set pieces and we were really efficient when we got them.
"It's always important to have a good start, especially at home so we get the fans going and get them to help us in the pressing situations."
The start to the game was pleasing to Asbaghi, who saw his side play a more proactive than reactive role early on, something he suggested had been a part of the game plan.
Asbaghi referenced the fact that The Reds have had no real issue with starting well recently, having had the lead in their last two games up until the final five minutes, where they dropped two points consecutively with draws against Stoke City and Fulham.
On The Reds' chance creation
"We were able to score with set pieces, which we know is an area we want to score in as well so we don't just depend on scoring counter attacks or open play.
"Today we really brought it out and that was the reason we won this game."
Set piece taker Amine Bassi can take a lot of the credit for the successful start to the game and for the new chances Barnsley created with corners.
Admittedly, they were given a helping hand by some lacklustre Bristol City defending, but for the Moroccan to have registered an assist and a key pass from corners both leading to goals, Bassi definitely played a crucial role in the victory for The Reds.
It was a good game for Barnsley to test their ability to score from corners, as visitors on Tuesday evening have a poor record when it comes to defending set pieces, which The Tykes were able to expose even further.
On The Tykes' resilience
"I'm happy that with the history that we have had of conceding those goals that we were mentally strong today to be able to overcome that.
"I'm impressed by the mentality."
The refusal to give up or ease off towards the end of the game is the mentality that Barnsley will need should they want to ensure Championship survival this season.
All to often The Reds have managed to find themselves in promising positions in a game only to throw it away, so the fact that his side were able to keep going for 90 minutes was pleasing to Asbaghi.
With time running out for The Tykes to escape the relegation zone, Asbaghi will be hoping that his side can continue to play in this way to give themselves the best chance of playing Championship football at Oakwell next campaign.
The Barnsley boss admitting that he was impressed by the mentality does suggest it was something he may well have been questioning after dropping four points late on across their last two games.
The emphatic response from the players to such doubts will have been well timed.
On keeping a clean sheet
"I'm happy that despite the tiredness we had [in the second half] that we still were able to defend this lead and keep a clean sheet at home.
"We have been pretty consistent in our defending in the at least the last month, we work pretty hard as a collective, we help to defend the backline."
The clean sheet was a deserved reward for Barnsley's defence for their significantly improved defensive showings in the last month.
Confidence and belief will be invaluable to The Reds as they approach the business end of the season with their survival very much so dependent on good performances in the run in towards the end of the season.
The Barnsley manager's comments were the complete contrast of opposition manager on the night Nigel Pearson, who voiced his disappointment towards his side's inconsistency.
The Robins headed into the game at Oakwell on Tuesday evening having beaten Blackburn Rovers at Ewood Park 0-1 in their first away win in five months, only to fail to really threaten The Tykes' goal for the majority of the game.
On Barnsley's home form
"We will not stay up in this league if we do not win enough games at home, that's how it is.
"We've been able to use the home pitch and the fans in the last few games in a good way, and that's a must for us to be able to stay up."
The Tykes find themselves unbeaten in their last five home league games following the result on Tuesday night, winning three and drawing two.
This is something that Asbaghi knows his side will have to be able to sustain in their bid for Championship survival.
He also said that he would have taken the five points Barnsley have gained from their past three home games before they were played.
However, due to the way in which they dropped the points late on, Asbaghi said his side were so close to getting all three points at home in their last three that maybe he suggested he was not as pleased with a return of five points as he would have been beforehand.
Ahead of Asbaghi's first South Yorkshire derby in charge of The Tykes, the 36-year-old admitted it would be a tough game, but also said that due to the confidence around the squad, the match is well timed for Barnsley.