The Reds surrendered a 2-0 lead at St Mary’s on Sunday afternoon as Southampton emerged 3-2 winners thanks to goals from Sadio Mane and Graziano Pelle.
Philippe Coutinho and Daniel Sturridge scored first-half goals before Ronald Koeman’s Southampton side surged back in the second half in the Premier League clash.
The 18-time English champions have conceded 40 goals in 29 Premier League games so far this season.
Former Arsenal striker Wright is confident that Klopp can improve Liverpool over the summer and the coming seasons.
“Under Jurgen Klopp, when Liverpool get it right in terms of how he wants to play, you can see what he is going to hopefully build for Liverpool and what they’ll end up like,” Wright told BBC Sport.
“They still have the frailties of before – the mistakes. That’s what he will slowly eradicate from Liverpool. It’ll take him some time.”
Liverpool are in ninth place in the Premier League table after Southampton hoisted themselves about the Reds thanks to their dramatic 3-2 victory.
The Merseyside outfit are in action against title-chasing Tottenham Hotspur at Anfield in their next Premier League game on Saturday 2 April.
The Reds are seven points behind fourth-placed Manchester City in the race to secure a place in next season’s Champions League.
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news