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A win against Everton would have piled the pressure on Manchester City in particular, who would have gone into its match with Brighton four points behind.
However, what was already out of Liverpool's hands is now reliant on a minor miracle, with neither Manchester City nor Arsenal looking at all likely to slip up to the required extent.
He sounded a dire warning that Champions League qualification is not yet safe, and admitted he "doesn't expect" Pep Guardiola or Mikel Arteta to lose twice.
"I am pretty sure City and Arsenal see it as a two-horse race," said Klopp after the Everton game.
While the Liverpool boss believed City would consider them out of content, the Spaniard has insisted that Klopp's team remains in a threat.
"Many things can happen," he said, via the Manchester Evening News.
"What happened to Liverpool dropping two games against Palace and Everton can happen to us and happen to Arsenal.
"Everton playing for their lives — like Forest.
One slip-up for Arsenal or Manchester City before the final day is far from inconceivable, which could at least make things interesting.
But Guardiola's side look to have found their run-in groove.
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