Carrick remarked how the goalkeeper "looked well" for his age, while O'Shea said it was "incredible" to think Edwin is still performing at the top level.
"It's a great achievement," Carrick said. "There are goalkeepers down the years who have played a lot later into their careers than outfield players, but to do it at this level and at this club is some going. And it doesn't seem like he's letting up any time soon."
"If he really wanted to, he could go on for another few years," O'Shea added. "But obviously that's down to him and there won't be pressure from anybody at the club to make him continue. But he's in great condition, looks after himself well and trains very hard. He's incredible – I definitely don't think I'll still be playing at 40."
O'Shea said on Friday morning that he expected Edwin to come in for some special treatment at Carrington later in the day.
"I think there'll be a big cake in the canteen," the Irishman said. "It's something of a tradition around here. And I'm sure there'll be plenty of jokes about the number of candles on it!"