The Whites fell behind just after the break as midfielder Paddy McNair opened the scoring with an emphatic finish. The Black Cats were pegged back by a lovely curled effort from Pablo Hernandez from just inside the area with 18 minutes to go before Gaetano Berardi saw red in injury time for a horror tackle on Callum McManaman.
Heckingbottom though believed his team deserved some credit for coming back in a difficult fixture but admitted he wasn't happy with a point.
"You can't be satisfied with the draw but you have to give the players credit for coming back," said Heckingbottom.
"We opened the game up and we knew we'd be giving Sunderland more opportunities, but we were hoping we would create more and we did. We have to give the players credit for that but I would have liked us to capitalise on those big moments early on because then it's a different game.
"We looked slick at times and Sunderland were a threat on the counter, they hit the bar from a set-piece and a lot of our best opportunities had to be really well worked.
"Sunderland had bodies behind the ball and they were keeping the ball in front of them, anything we did get was going to have to be eye of the needle stuff. Whilst it looked really good I thought we were limiting the amount of opportunities that were available to us.
"We had to take the risk that we were going to open the game up."
The Whites manager handed a debut to 20-year-old central defender Paudie O'Connor on Saturday afternoon and admitted he was impressed with the young Irishman's performance.
"He can be pleased with that," said Heckingbottom.
"In fairness to Paudie when I made the change I was exposing him to a lot more one on ones, we went three at the back which meant he was going to have to be confronting the winger a lot more than he would've liked but he'll be better for the experience, definitely."
Questioned over Berardi's red card, which is the Italian's third of the season and United's eighth at a team, Heckingbottom said: "I'm upset about that and frustrated."
"Berra is an honest person, I questioned if he lost his head, but he's genuinely going for the ball and he's accepted it was a bad tackle."
Sunderland boss Coleman believed that it was the correct decision and also revealed that he thought Paudie O'Connor was lucky to stay on the pitch for his tackle on Lynden Gooch earlier in the game.
"That's a straight red," said Coleman.
"The one earlier on Lynden Gooch as well on the far side, if you don't jump out of the way I dread to think. Being a defender myself I was no angel but I call it as I see it.
"Callum McManaman has stud marks right down his shin from his knee to his ankle. It's a straight red, the kid has got it wrong."