Lacazette was heard screaming as he was tackled by Erik Pieters in the second half of Saturday’s 1-1 draw at Turf Moor – though he was soon back on hit feet.
Later that night, Gunners legend Wright joined in with presenter Gary Lineker and fellow pundit Dion Dublin as the trio mocked Lacazette.
After a number of other jokes at Lacazette’s expense, Lineker signed off the show by saying: “We’re all off to practise our screaming.”
The three then yelled out as Lineker pretended to collapse off his chair while holding his leg for dramatic effect.
Wright says he has had always had a problem with players reacting to challenges in the way Lacazette did – which of course is now much more audible to television viewers with no fans in stadiums.
But he admitted it was a mistake to join in with the screaming at the end of the show given his standing among Arsenal fans, and apologised for “digging out” Lacazette.
“The main thing here is that I got that wrong,” said the former Arsenal and England striker on Wrighty’s House Podcast.
“It’s only the screaming at the end. The fact is that screaming has always been a problem for me with the guys.
“Now we can hear it and we’re talking about massive screams to the point where you’re thinking, ‘Oh my God, something’s wrong with this player!’
“This week it just happened to be Lacazette and, like I say, I got that wrong but what I did, when you see all the s*** that comes back… and in hindsight, of course the s*** is going to come back, especially with the fact it was an Arsenal player and it’s me.
“And me and Laca go back and we’ve got correspondence.”
Wright revealed he had contacted Lacazette to apologise, saying: “I got in touch with him on Sunday morning so we could clear it up.
“The way it was portrayed on social media, the way it was and it was Laca in that particular incident, it seemed it was digging out Laca. But we were digging out the screaming.
“My biggest mistake was the screaming at the end. F****** stupid and at the end of the day, it’s not a problem for Gary Lineker or Dion Dublin.
“But at the same time I have to accept and realise what that means to the Arsenal fanbase and what that means to me for them to feel like one of their own is supposedly digging them out.
With the Cheltenham Festival only just around the corner, we are giving you the chance to sign up to our free updates ahead of one of the biggest weeks in racing.
Racing Digest will give you daily updates around all the big stories – including tips, offers, results and much more. To sign up, simply put your email into the box below, and we’ll do the rest. You’ll also receive plenty of tips and info outside of Cheltenham too… after all, the Grand National isn’t far away either.
So get signed up, join our club and get ready for the inside scoops on the greatest week in jumps racing.
“I can only say I was digging out the screaming. We’re talking about people that are screaming, they get up and then they play on.
“If he stayed down or if a player stays down, let’s talk about Raul Jimenez. As we speak, we don’t even know if he’s going to play again so I don’t want to make it too much of a massive thing but the screaming, for me, from anyone is not necessary.”
Sean Dyche mocked the Gunners striker at full-time after Saturday’s match, while Arsenal boss Mikel Arteta hit back by accused Burnley of trying to “weaken” his players.