Dyche made a host of changes to his side for the second-round clash against the Black Cats, and it came back to bite him as the League One side came out on top.
Drinkwater joined the club on a season-long loan from Chelsea earlier this month and was handed his first senior start since March 2018, but it proved a debut to forget for the former Leicester man.
In trying to cut out Denver Hume's innocuous pass, Drinkwater deflected the ball into the path of the unmarked Will Grigg in the area, and the Northern Irishman duly grabbed the lifeline to cancel out Jay Rodriguez's opener.
However speaking after the game, Dyche said Drinkwater cannot be judged on one performance alone and needs to be given time.
"I'm not really going to question Drinky, we know he needs football, he knows he needs football as well," Dyche said. "He hasn't played a lot, he's getting used to the players around him so that's a different thing.
"He stuck at it, he's got through the 90 minutes which is really important. I'm not really judging him in amongst our pack, that's for sure, not just on one performance.
"He's tried to be diligent, tried to be honest. It's not just down to his mistake, we weren't quite sorted out to stop it, even with a mistake."
While Dyche retained only Dwight McNeil from the weekend draw at Wolves, his Clarets line-up contained a number of former or current internationals, including Joe Hart, Aaron Lennon and Rodriguez.
Rodriguez marked his first start since rejoining his hometown club over the summer with a calm finish as Burnley largely dominated in the opening 45 minutes, only to be pegged back by Grigg.
Burnley were then caught cold on the resumption, with Tom Flanagan and George Dobson scoring for the Sky Bet League One side within five minutes of the restart.
Dyche added: "That's a really experienced team we put out there, I should have enough faith in that to get through 95 minutes.
"That's probably the head-scratcher because that's probably the most experienced team - when I have changed the team - I've put out in my nearly seven years here.
"When you look on paper that's a strong outfit. We should be taking care of ourselves better than that.
"In the first half I thought we were in complete control in every area other than the mistake. For 35 out of 45 minutes in the second half we just didn't turn up."