Liverpool had won three Premier League games in a row to raise hopes of European qualification, but produced a ragged performance at St Mary's, particularly in the first half.
Rodgers was disappointed with the goals his side conceded on the South Coast and admitted Liverpool did not get going until they were 2-0 down.
"I thought Southampton deserved to win," Rodgers told Sky Sports. "We were nowhere near what we've been in the last number of weeks.
"It's very difficult at this level whenever you make the start we made today of being two goals behind. We only started to play when it went to 2-0.
"The three goals conceded were disappointing goals today, but in between the second goal and the third goal we were very good.
"We got to 2-1 just before half-time and had more fluency and flow in our game. We created chances, but then conceded a poor third goal that was far too easy and from that perspective it was bitterly disappointing."
The international break means Liverpool do not play for a fortnight and Rodgers wants a positive response in the next game at Aston Villa.
He added: "I said before the game that this game was arguably going to be one of the toughest games for us this season and overall I can't complain.
"We weren't at our best and we're not the sort of team yet when, if we're not at our best, we can see through results.
"We have to lick our wounds for a couple of weeks before the next game, and we have to make sure it was a one-off and we get back to how we were playing, at a real high level and with confidence."
All this fuss about whether Suarez stays or not, no team in mid table can afford to keep a player like that when there are so many areas that need to be strengthened. Who else outside the top four, has a 40 million pound player in their team? If the team were 5th and only one or two short of top four, fair enough, but this team needs another 3 or 4 players, and can get them if they take the best offer for Suarez. Rodgers has got the team to where they are despite him, not because of him.- Gab1965