Liverpool boss Brendan Rodgers said he found Southampton fan's disrespect of former players Adam Lallana and Rickie Lambert "disappointing".
An exceptional strike from Phillipe Coutinho and Raheem Sterling's second-half effort gave Liverpool the win they needed to make seven victories out of their last 10 league matches.
Rodgers wasn't happy with the reception former Southampton players got at St. Mary's, however, with no mention of the players in the programme – although there was a mention in the club captain's notes – and fan's boos towards Lallana.
"Adam was the captain here for two years, gave incredible service to Southampton and I know for a fact he could have left here a number of times and didn't," Rodgers said.
"And to get the reception he got, I thought was disappointing. I looked in the match programme and there was nothing relevant to his time here and all the time has been here since a boy.
"Then there's the likes of Rickie Lambert - great servants to here, incredible players that have got the club to where it is today. There was no mention of him, which I thought was sad.
"I can see Lovren because he was only here a year, but those two guys gave their heart and soul to Southampton and are big supporters of this club.
"They've moved to one of the biggest clubs in the world, so it is hard to deny a player that. I thought they could have been given a wee bit more today."