Claude Puel said Southampton have "a lot of regrets" after failing to make the most of their opportunities against Manchester United on Friday.
Southampton lost 2-0 at Old Trafford as Zlatan Ibrahimovic's brace inspired United to their second successive Premier League victory to start the season.
The visitors, however, were not without their chances in Manchester, after Dusan Tadic found the back of the net in the second half but his goal was ruled out for offside.
Speaking afterwards, Southampton boss Puel lamented: "We have a lot of regrets, because we had many situations and created some good opportunities, but we didn't take them and score.
"Perhaps in the first 15 minutes it wasn't good, but after I think we played a good game, with good football and good possibilities.
"We played with quality, good control and good passes and had many situations which is positive, but we needed to take one of them, of course.
"Now we have to correct many details, defensive also. It's difficult to take this first goal, because we have some situations before Manchester United.
"The second goal was also difficult to take just at the start of the second half. It allowed United to play on the counterattack.
"We continued to play. It's important now to correct some details, but there were positives for the future. We have to score when we create the chances."
Southampton settled quickest of the two teams at Old Trafford, however, the deadlock was broken by Ibrahimovic in the 36th minute, rising highest to head home Wayne Rooney's cross.
And the former Sweden captain doubled the lead from the penalty spot shortly after half-time, following Jordy Clasie's foul on Luke Shaw.
Southampton have collected one point from their first two matches after their 1-1 draw against Watford last week, and forward Shane Long has already turned his attention to the visit of Sunderland.
"Last week was disappointing because we should have won, and then we could have scraped a draw at Old Trafford on Friday," Long added. "Next week is now a big game for us. If we can get the win there and a few goals, it will give us a positive outlook again and then we can kick on from there.
"We need to try and make St Mary's a difficult place for opposing teams, many of whom come hoping for just a point. Our form at home could really push us up the table. But we have to take every game as it comes. Sunderland will probably come and sit in and make it tough for us offensively. So we're going to need to be really up for the game."