Liverpool trailed Crystal Palace 1-0 but came back to win 2-1, playing their best football with 10 men.
And Allen told the BBC: "The amazing thing is that Milner's exit hasn't changed the encounter at all. Palace have not dominated and have not used their man advantage at all.
"If you look now at Jurgen Klopp he is out in the technical area screaming at his players. I think, even with 10 men, he's going for the win here..."
He later added: "This whole game has turned on the Milner sending off. The changes made by Klopp have made the difference and the 10 men left on the field played with much greater intensity.
"I have to say, though, they have deserved it. Liverpool have been the better team in this second-half."
Milner had a good game against Manchester City earlier this week, while his career so far with the Reds has produced plenty of hard work and several good moments.
However, the 2-1 win over Crystal Palace sums up a huge weakness with Milner. Indeed, for all of his 'hard work' and endless running around, what does the midfielder actually offer Liverpool?
Is it possible that, by using up so much energy, he is draining energy from the Liverpool side? Every time Milner is given the ball, he runs and runs and runs. But what does he do with the ball?
The Reds were better with one less player than with the 30-year-old! Imagine how much better they'd be with a player who actually has an end product?