Gayle, now with Hibs, made the claim last week.
He recalled a game in 2020 when Newcastle had lost 5-0 to Manchester City on the Open Goal podcast: "I remember like some of the boys got chucked into the Man City shift, basically.
"We had like a three-game week, and I think the gaffer sort of chucked a few of the boys under the bus in terms of who had to play against Man City away.
"And me and Matty Ritchie were asking for tactical improvements for weeks or months or whatever.
"And then we come in at half-time, and I think we were 2-0 or 3-0 down, and he's like, 'Boys, you keep asking for tactics – I don't do tactics! Just put your boots on and work hard'."
But Bruce has now responded, telling BBC Radio Lancashire: "Is that the legendary Dwight Gayle, who missed the chance in the quarter-final against Manchester City? Is that the same Dwight Gayle? Interesting.
"I've been around the block a long, long time. I've only managed 1,050 games but according to Dwight, I don't know what I'm doing.
"I'll let other people make their minds up who are a bit more established than Dwight ever was."