The Reds' faint top-four aspirations took a blow at St Mary's on Saturday as Morgan Schneiderlin, Rickie Lambert and Jay Rodriguez consigned them to a 3-1 defeat
Morgan Schneiderlin and Rickie Lambert gave the Saints a two-goal lead at St Mary's and Philippe Coutinho's goal was cancelled out by a late strike from Jay Rodriguez.
The Reds were without Jamie Carragher for the match on the south coast and have now conceded more goals away from home than any other top-half team.
"We just weren't very good," Rodgers told reporters. "We only started playing when we were 2-0 down. We didn't defend well enough and you have to give credit to Southampton, who played very well.
"When the team starts as it has done, it is always difficult. There's no question that [defence] is an area of the field we need to be better at. That is one of the reasons we brought Carragher back. I know it is one area we need to improve and develop as a group.
"We were unfortunate this week that a few of the players had niggles and missed training, like Lucas, who came on in the second half was excellent.
"It was a poor day at the office and the problem is we have to live with that for two weeks now [due to the international break]."
Rodgers acknowledged that the Reds had been left under no illusions regarding their shortcomings as they seek to rejoin the top flight elite.
"Today is a reminder that we still need to build a squad and need to improve," he added. "The players can't be brilliant every time they play. There are eight games left and we just have to concentrate on ourselves."
Southampton boss Mauricio Pochettino, meanwhile, claimed he was unsurprised by his team's performance as they moved seven points clear of relegation.
"The players don't really impress me because I know them and how good they are," he insisted. "What's really important is they show their talent in all the games.
"I think we set out the game in a positive way, and I think the players totally believed in our system. We made Liverpool really uncomfortable, pressed them quite a lot and played a lot high up the field in their half."
The Argentine coach reserved special praise for young defender Nathaniel Clyne, who turned in an impressive display against the likes of Coutinho and Luis Suarez at right-back.
"He has the potential and skill to one day play in the national team, if he keeps on playing like he did," Pochettino said.