The Reds were 2-0 up in the first half thanks to goals from Philippe Coutinho and Daniel Sturridge at St Mary’s.
Two things are important – we didn’t get the points and that’s not too good; on the other side, we saw how well we can play football, which we should not forget
Joe Allen had a goal ruled out for offside, while the Wales international and Sturridge wasted chances to extend Liverpool’s lead before the break.
Southampton mounted a second-half comeback after Sadio Mane halved the deficit before Graziano Pelle levelled with six minutes remaining.
And Ronald Koeman’s side became the first Premier League club to overturn a 2-0 half-time deficit against Liverpool and win thanks to Mane’s late goal.
But former Liverpool manager Klopp was determined to remain positive despite the disappointment of Sunday’s 3-2 loss.
Klopp told Liverpool’s website: “We can say we have to have more killer instinct in the first half or we have to play better in the second half. Both are true and both we will try in the future.
“Two things are important – we didn’t get the points and that’s not too good; on the other side, we saw how well we can play football, which we should not forget.
“I know the result is not what we wanted but we have to accept it this season, we have to take what we can get and not think always now the top four, ‘yes, no, perhaps, I don’t know’.
“Play football like we did in the first half, score goals and everybody will enjoy it and then everything is OK.”
Liverpool are in ninth place in the Premier League table after Southampton hoisted themselves above the Reds thanks to their 3-2 home win.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news