The Albion midfielder equalled Gareth Barry’s Premier League appearances record of 653 when he got on midway through the first half at Aston Villa.
As an 18-year-old, he played alongside Shearer at Newcastle.
That was highlighted as the latter spoke on a midweek edition of BBC TV’s Match Of The Day.
The former England striker said: “He's the consummate professional, he really is.
“He was always last on the training ground, always working incredibly hard.
“And it's no surprise to me and to everyone else that has played with him over the years, that he's still actually going.
“He's going because he's got an incredible attitude and you have to have that to stay in the game that long.”
Milner is the only player still active from Shearer’s own days playing in the Prem.
He added: “That's why he needs to carry on. Carry on for a few more years, James!”
Fellow pundit Danny Murphy highlighted the fingertip save from Emiliano Martinez which he felt did enough to divert Ferdi Kadiogu’s shot on to the crossbar at 0-0.
Murphy said: “You need the small moments to go for you, and they have got a wonderful goalkeeper who is capable of producing brilliant saves.
“He did a couple at Bournemouth, actually, at the weekend.
“But, when you actually look at this back, it's a good effort from Kadioglu. It's an unbelievable save.
“We'll see it in slow motion and you'll see the fingers he gets on it.
“We know he's got this. Time and time again. He's one of the best keepers in the Premier League.”
Murphy highlighted Albion’s run of one win in 13 league games which has turned the spotlight firmly on head coach Fabian Hurzeler.
He said: “The level of performance has been nowhere near and Brighton's level of expectation from the supporters now, and even the hierarchy, is higher than it has ever been.
“So he has got to pick up some results soon and pick up form, otherwise, they'll move on to the next manager.”