The Reds were on course for a third successive win at Oakwell and third victory in four Championship games to further revive their survival fight, thanks to a brilliant 70th-minute curler from Domingos Quina, who followed up his eye-catching strike in the recent home game with QPR.
But Stoke produced a stunner of their own to level in the fifth minute of stoppage-time through Lewis Baker, in a game where there were nine minutes of added-on time following an incident in the Pontefract Road stand in the second half.
Asbaghi was also disappointed that the Reds were not awarded a penalty in the second half.
Remy Vita went down in the box early in the second half, but referee Leigh Doughty was unmoved and the Lancastrian also rejected strong home appeals for a late spot-kick when Quina nut-megged Taylor Harwood-Bellis before going down in a heap following an untidy looking challenge by the Stoke player.
Asbaghi said:: "It feels like a loss of course. It feels tough at this moment.
"The first half was not one we really wanted.
"Stoke played more direct than we expected and pushed us down with direct balls and creating a lot of set-pieces. We came into half-time and felt we needed to be more aggressive and to have something more to see in the game.
"We got what we wanted in the second half. It was much more even and then we scored a really good goal from Dom to make it 1-0.
"We had two situations with penalties and did not get that and then in the last minutes, we conceded a goal and of course, it is a tough one to concede.
"I have not seen them (penalty calls( again and I stood pretty far away and it looked suspicious from my side.
"I am not the one to decide. Let's just say that we have not been so fortunate during my time here in getting these 50-50 situations with penalties and we have to work hard to get them on our side."
Despite his disappointment with his side not earning a penalty, Asbaghi felt his side only had themselves to blame in failing to clear their lines and averting the danger ahead of Baker's strike, with Claudio Gomes and Devante Cole being culpable.
He added: "I believe we had ten players before the ball and they were still allowed to score and we need to do that better and only have ourselves to blame for conceding that goal.
"I don't want to point out individuals and that's something we will do behind closed doors. But of course, I am disappointed with the way we conceded the goal."