However, that does not mean they will be taking their eye off the ball in terms of chasing a first domestic league title in 29 years as the vice-captain feels they believe they can compete on two fronts – even if the critics do not.
The 3-1 defeat to Real Madrid in Kiev last May was something of a freak result as Jurgen Klopp’s side were the better team until Mohamed Salah was forced off with a shoulder injury suffered during a tangle with Sergio Ramos.
Goalkeeper Loris Karius, suffering from concussion after an earlier blow, had a meltdown for two of the goals, with the other a fantastic overhead kick from Gareth Bale.
It left Liverpool with a feeling of missed opportunity, and a degree of injustice, something Milner wants to put right.
“I don’t think we think about that too much at this moment in time but it is a memory that never goes away too quickly. You still think about it now,” he said.
“Maybe – hopefully – if we get to the final, we can think about putting it right then.
“We probably took more positives from last year than negatives but it’s a bitter pill to swallow when you lose the final of the Champions League and the way we went down.
“You are proud to have played in the European Cup final but you don’t go there to lose.
“Listen, I have loved every minute of my time at Liverpool but to have not won something when we have given ourselves opportunities is difficult to take at this moment.”
Liverpool still have two chances to win a first trophy since the 2012 League Cup and first under Klopp.
The title race is still too close to call and Milner believes progress in Europe will help rather than hinder domestic progress.
“You know, it’s been so long since we won a league title. Even in recent years Liverpool haven’t won as many trophies as they should do for such a big club,” he added.
“Even for us now – we are a young team, we are improving but the chances we have given ourselves? We have to put that right.
“We have to get over the line in one of them.
“But (we can use) the thoughts of the run we had, the teams that we beat and the confidence that we gained.
“Then you see how we are playing in the Premier League – we have only lost one game – that is confidence and helping us move forward as a team.
“We are in two competitions and we can manage that, game-wise. There is the good feeling you get from winning in the style that we did (in Munich), the confidence going into the weekend.
“We got a good feeling from getting out of the group and we have got a good feeling after knocking out Bayern Munich. You can only take positives.”
Liverpool remain a team few will want to be pitted against in Friday’s quarter-final draw because of their recent record in the competition.
Even Manchester City manager Pep Guardiola’s support for Bayern in the aftermath of his own club’s qualification for the last eight on Tuesday was as much about not having to face their north-west rivals as it was about his former employers.
“Ah, yes. That’s unlucky for him, isn’t it?” said Milner with a wry smile.
“I’d like to think teams have that respect for us.
“Whether teams take notice is not really for us to worry about but they take notice after they have played us and we have put them out.”