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The former Gunners forward, who was joined by presenter Gary Lineker and co-pundit Dion Dublin in the studio on Saturday, poked fun at Lacazette for his theatrical reaction to a tackle from Burnley defender Erik Pieters in the 1-1 draw at Turf Moor.
Wright, alongside Lineker and Dublin, then decided to re-create the moment on Match of the Day by screaming loudly and holding their legs.
You can see the footage below.
Following the show, Wright said he felt the need to contact Lacazette personally.
On his podcast Wrighty's House Podcast, the 57-year-old explained his decision to get in touch with the Frenchman because of their friendship off the pitch.
"The main thing here is that I got that wrong," he said.
"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."
It's amazing that scream from Lacazette could be heard all the way in London. I'm glad he was ok to chase the ball straight away embarrassing. hate it when players do that.- Lianne Sanderson (@liannesanderson) March 6, 2021
That Lacazette scream gets more embarrassing the more you hear it- Kelvin Stuttard (@kelvinstuttard) March 6, 2021
Wright later revealed that both he and Lacazette cleared the air following the dramatic re-creation on the show.
"I got in touch with him on Sunday morning so we could clear it up," he added.
"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."
Wright continued, saying: "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."
Thoughts on the incident on Match of the Day last weekend?
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Featured Image Credit: PA/BBC
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