Rodgers: Liverpool didn't defend well enough
Last week's 3-2 win over third-placed Tottenham Hotspur had given rise to renewed optimism at Anfield but Liverpool were outplayed for long periods by a Southampton side easing away from the relegation battle.
"We just weren't very good," Rodgers told reporters. "It was as simple as that. If you start games as we started it is very, very difficult at this level to get back.
"We got it back to 2-1 but then conceded another very poor goal for the third goal. If you concede the goals we conceded today it is always difficult to win games.
"We were offensively bright and created chances and could have scored more than one goal but we didn't defend well enough and you have to give credit to Southampton as well."
Southampton were 2-0 up after little more than half an hour thanks to Morgan Schneiderlin and Rickie Lambert but Philippe Coutinho replied on the stroke of half-time with his second goal since joining Liverpool.
Jay Rodriguez then sealed Southampton manager Mauricio Pochettino's second league victory since taking over from Nigel Adkins in January - the other was also by a 3-1 margin against Manchester City.
"I think we set out the game in a very positive way and more than anything the players believed in how we wanted to do it," Argentine Pochettino said.
"We made Liverpool very uncomfortable, we pressed them a lot and put in a very big effort and that is the way we want to play, high up the field in their half."
Liverpool remain in seventh spot, seven points behind fourth-placed Chelsea who have played two games fewer.
While not conceding defeat in the race for a European spot, Rodgers said the rest of the campaign was about building for next season.
"There are still a number of games to go, it's about us concentrating and keeping our focus on each game. We can't get too far ahead. There is still a lot of work to do," he said.
"Today is a reminder for us that we still need to build our squad and improve. The players have been brilliant but sometimes you are not perfect every time you play."