Southampton boss Mauricio Pellegrino felt his side should have pushed for a second goal to kill the game before Albion equalised in the 1-1 draw at the Amex this afternoon.
The visitors took the lead on seven minutes when Steven Davis headed home the rebound after James Ward-Prowse's free kick came back off a post.
Albion struggled to get going in the first half but Saints did not create any clear chances to double their lead and Brighton equalised on 52 minutes when Glenn Murray headed home Pascal Gross's cross.
Pellegrino said: "We got the early goal and made a good start, so we are a little bit disappointed as we were in front and they scored.
"After that, when you allow the opponent to come back and be in the game again, in the Premier League every single team has quality to create problems.
"To play against Brighton away is not at a good moment because they are mentally really high and their motivation to play for every single point is really high on this pitch.
"My feeling right now is we competed well but when we are controlling this type of situation, you have to play with more determination to score the second one and maybe kill the game.
"In the first half, we could have gone forward with more determination. In the second, we expected a reaction and they obviously were pushing and after they equalised we controlled the ball but we never found the situation to score the second one.
"From the bottom of the table up to sixth or fifth, the difference is not too high. You have to fight for every single point."
On Albion's goal, when asked if Southampton keeper Fraser Forster could have kept out Murray's header, Pellegrino said: "It was a bit unlucky because the ball I think deflected off the defender's head so surprised the goalkeeper a little bit.
"Thats part of football sometimes. From outside, every single action looks simple but from inside, football is the vision and every single action is completely different."