The England right back made the admission during a recent in-depth interview with a popular football podcast.
A star of the Three Lions’ 6-2 opening game win over Iran on Monday, Trippier was a guest of UndrTheCosh, a weekly podcast hosted by former footballers Chris Brown and Jon Parkin alongside comedian Chris Brown.
Wallace, who played 36 times for the Hoops, was a former team mate of Trippier during his time with Burnley and the 32-year-old, who now lines up for Premier League high flyers Newcastle United, spoke at length about the bust up with the former Celtic youngster.
"I think it was Heats (Tom Heaton) who was kicking the ball out and he (Wallace) was pulling my shirt – I asked him what he was doing and as I turned back to him he’s given me a f***ing little nut in the eye. I’ve still got the scar now above my eye. We had it out on the pitch.
"One thing I didn’t like about that was he did it when I wasn’t looking. So we had it out – and then it was alright after that.
"It was one of them. In the heat of the moment you want to have it all out on the pitch. I went in to get it stitched and, to be fair, he came in and apologised. It was one of those where it is just not worth it.
"Dychey (Sean Dyche, then Burnley manager) was fine. He wouldn’t jump in, he was just like let them have it”.
However, the Magpies player confirmed that the duo had long made amends with Trippier saying Wallace was often the dressing room prankster.
"Ever since then, we’ve been fine. He is good banter. He’s a great guy to be fair Ross. Those incidents happen all the time in football. You just get on with it”.
The full episode of the podcast, which lasts for a mammoth one hour and 22 minutes can be listened to via this link.