The Celtic captain was visibly emotional after his spot-kick was saved as Aberdeen won the Scottish Cup at Hampden.
McGregor was consoled by Kasper Schmeichel and Scott Bain before he was seen being comforted by manager Rodgers.
Rodgers could be seen in discussion with McGregor after the defeat as he hugged his captain.
Rodgers said: “He’s such a conscientious guy who gives so much to this club. As the skipper, he’s obviously so disappointed he hasn’t scored.
“I was just reminding him what an incredible leader he is for this club. He’s given so much to this season and to all the seasons that I’ve ever known him. He is such an amazing guy.
“It’s unfortunate the keeper makes the saves. But no, he’ll come back in the summer stronger, fitter and ready to go again.”
On Kasper Schmeichel’s error as Aberdeen equalised, Rodgers added: “He’s obviously apologetic to his teammates, but he’s been outstanding for us all season.
“It was one of those moments in the game late on that can happen. We still had one or two other chances that we could have scored from, but, yes, it was just unfortunate at that time of the game.”
