Scholes, reflecting on Arsenal's 2-2 draw at home to Swansea City, claimed Wilshere "doesn't look any better now than he did when he was 17" and had failed to reach the "next level".
Wilshere requested Scholes' number from England coach Gary Neville, sat beside Scholes during his remarks, and received clarification from a man he considers to be "the best English midfielder of all time".
"It was a bit strange, out of the blue," Wilshere said. "I remember watching it, he was having a go at Arsenal, and I was thinking 'Is he going to come for me?'
"I actually spoke to him after. We had quite a good chat. He is entitled to his opinion but I just wanted to know. If it had come from a rubbish player I could say 'what are you talking about?' But it came from Paul Scholes.
"So I wanted to get to the bottom of it. I spoke to him, he explained it a bit better and told me what he thought I should work on. For me he was the best English midfielder of all time."
Scholes suggested Wilshere had stagnated due to Arsenal's flimsiness and lack of personalities.
"When Jack Wilshere came on the scene, what a top young player he looked," suggested Scholes, making his Sky Sports punditry debut. "Injuries haven't helped him, but his development from 17 years of age, he doesn't look any better player now than he did when he was 17.
"He needs people like [Patrick] Vieira, characters like that, to take him on to the next level. Characters and leaders are important. You play Arsenal now, get stuck in about them and you've won the game."
Wilshere, selected in England's 23-man World Cup squad, accepts he must now fulfil his widely acknowledged potential.
"(Scholes) was right in a certain way," he said. "When I first burst onto the scene there was all this noise and then I got injured.
"I have had bad luck with injuries but I can't keep saying I've been injured a lot. There comes a time when you stop being a kid and I think that's what he's referring to. 'He's young, he's got all this potential ' - you have to start putting that potential in.
"This season I have improved a lot, scored a few more than I have in the past and got a few more assists.
"That side of things, you can keep the ball and you can look good but it's those stats that matter. That's what I have to build on."