There are just three matches remaining in the Reds quest for an unprecedented quadruple.
Jurgen Klopps side kept those hopes alive by repeating Februarys Carabao Cup win on Saturday, with a goalless 120 minutes followed by another penalty shoot-out victory against Chelsea in the FA Cup final.
The Reds will lock horns with Real Madrid at the Stade de France in the Champions League final on May 28, but first comes their final Premier League matches against Southampton and Wolves.
Milner knows former club Manchester City have the upper hand in the title race, but feels a second-placed finish would not take the edge off an unforgettable Liverpool campaign.
You guys can keep talking about it, he said of the quadruple. For us, we just need to take a game at a time like we have done all year.
We have three games left. We will try and win them and see where that takes us.
We know its in Citys hands. Theyre in a good position and theyre a relentless, very good team.
So, for us to be where we are at this point in the season, to have two trophies in the cabinet and to still have a glimmer of hope in the other two, its been a special season no matter what.
But we want at least one other piece of silverware.
Milners second FA Cup triumph came 11 years after his first win, with the veteran coming off the bench in the second half of Saturdays match to add to energy and experience in midfield.
Asked what Klopps message to him was when replacing Naby Keita, he said: Just use your experience and try to get the energy and aggression into the game, but also be calm when weve got the ball.
That was the message and thats what we tried to do. Go in and try to lift the guys.
Theyve played so many games, the effort they put in continually.
You could see the fatigue out there, a couple of niggles as well, a couple of the boys coming off and things like that.
The effort and workload the boys have put in this season has been an incredible, the amount of games theyve had.
I cant speak highly enough of the attitude and the drive within the dressing room to keep going, no matter whats happening, no matter how the game is going, the fatigue, mentally.
They just keep going and going, pressing into extra-time and the boys up front pressing.
This is a special group of not only players but staff as well. Its a special group.
That steely drive means FA Cup celebrations remained sensible as Klopps side turned attention to Tuesdays league trip to Southampton.
He knows that the boys are bang at it, Milner said.
Youve got to celebrate it, youve got to enjoy it but obviously weve got another game coming up quickly, like its been all season.
All season its been the same another game to concentrate on.
The mentality of the boys has been so good to be able to refocus and go again.