Liverpool fans rarely cheer on the other English sides in European competitions, but there was a sense of disappointment this week at the defeats for Manchester City and Arsenal against Real Madrid and Bayern Munich respectively.

Had the Premier League duo progressed, they would have met one another in the last four of the competition. And as Liverpool knows well, playing in a Champions League semi-final — against anyone, let alone a title rival — is usually a physically and mentally draining ordeal.

It would undoubtedly have been a boost for the Reds' chance of coming out on top in the Premier League had the two teams that it is competing against, but it wasn't to be. All hope, however, is not lost.

Manchester City lost on penalties against Real Madrid, meaning it had an extra half an hour to play. And Pep Guardiola's two key men, Kevin De Bruyne (coming off after 112 minutes) and Erling Haaland (replaced on 91 minutes), were simply too exhausted to continue.

"They asked me to go out," Guardiola said on his decision to substitute De Bruyne and Haaland. He added, bluntly: "They could not continue."

Recently, Rodri asked if he could sit out the game with Luton Town in the Premier League because of fatigue. And while Manchester City has not suffered with injuries to anywhere near the extent that Liverpool has this season, Guardiola does like to work with a smaller squad. The Etihad side does not have the depth that many assume it does.

This weekend, it will be interesting to see who makes Guardiola's starting line-up for the FA Cup semi-final against Chelsea. Just three days after a grueling two hours plus penalties against Real Madrid, Manchester City must take to the field at Wembley.

As Liverpool found in 2022, competing on all fronts is near-impossible to maintain. The after-effect of that long season was a campaign of extreme difficulty in comparison, and by the end, the physical exertion begins to catch up on you.

So while Manchester City has the lead in the Premier League title race, perhaps there is a glimmer of hope. Matches against Brighton, Nottingham Forest, Wolves, Fulham, Spurs and West Ham might not look the hardest run-in on paper, but with tired bodies and minds, plus the pressure of being in the lead without players like Riyad Mahrez and İlkay Gündoğan, who have been there and done it before, perfection will not be straightforward.

That is not to say that it will be for Liverpool either, of course, with games against Fulham, Everton, West Ham, Spurs, Aston Villa and Wolves remaining, and it remains the case even after the 1-0 win over Atalanta that the Reds must improve their form to even have a chance. But Manchester City has had a lot of matches to get through, and even now it is out of the Champions League, all hope is not lost.

We are very much inside the final run-in as Liverpool competes for the Premier League title, and it is not just Manchester City that the Reds must better, but Arsenal too. Win six out of six, though, as attention switches exclusively to that rather than trying to book a place in Dublin, and the signs are there that Jürgen Klopp's side might just have enough.