Liverpool midfielder Thiago Alcantara says Jurgen Klopp's men will keep "fighting for a small miracle" to make the Champions League places after scoring his first goal for the club in the win against Southampton.
It is a victory that puts pressure on fourth-placed Leicester City, who lost 4-2 to Newcastle United on Friday.
Klopp's men took full advantage of Leicester's defeat by moving within six points of the top four - and have a game in hand on the Foxes.
Sadio Mane opened the scoring against his former club, heading home Mohamed Salah's cross moments after Alisson had made two saves in quick succession.
Alisson gifted Southampton a chance to equalise late in the game when he passed straight to Che Adams, but the Brazil goalkeeper made amends by saving the Scotland striker's shot.
Spain midfielder Thiago then scored his first Reds goal in stoppage time to hand Klopp his 100th win at Anfield in all competitions as his side earned a welcome clean sheet despite having the inexperienced Nathaniel Phillips and Rhys Williams as their centre-back pairing.
"There are small chances. We are realistic with our situation," Thiago told BBC Sport about his side's top-four hopes.
"The most important thing is the three points. We dominated the game and created a lot. If you can help with a goal it's more than welcome."
