Hull City reaction: Leonid Slutsky slams first half show and promises to start goalscorer David Meyler
Hull looked to be heading to a third straight defeat until Meyler found the net late on.
Sunderland striker James Vaughan had earlier put the Black Cats on course for victory despite missing a week of training through illness.
Former Russia manager Slutsky said: "David Meyler missed four months (with a knee injury), he's really not ready to play every few days because we are waiting for his optimum fitness.
"In one week, no problem, but every few days it's very difficult. Today he only played 45 minutes and changed the game.
"We played two different halves. The first half was terrible, the second half was much better.
"I'm sorry for the first half, but in the second half, anybody who sat in the stands today would be satisfied by our second half.
"Believe me, everybody tried 100 per cent to succeed. We can play better and better. We are working very hard to try to change the situation."
Sunderland boss Simon Grayson praised Vaughan after the striker emerged from his sickbed to score his first goal for the club against Hull.
Vaughan, a summer signing from Bury, has been laid low by diarrhoea of late but led the line well at the KCOM Stadium in Lewis Grabban's absence.
The result did bring an end to Sunderland's four-game losing streak in the Sky Bet Championship, though, and Grayson was satisfied with the performance of his forward.
Grayson said: "Vaughany was in bed Thursday night and all day Friday with sickness and diarrhoea, so he was on his last legs in the last 15 minutes.
"I'm really pleased for him that he played and got his reward with the goal as well.
"I'm disappointed but pleased (with the team's performance) as well. We were very comfortable and dominated the ball, created some good chances and got the goal.
"We didn't pass the ball and retain it as well as we should do but we limited them to few opportunities. I think we just ran out of steam a little bit."