Koeman remains under intense pressure at Everton following a poor start to the campaign, not helped by this 1-1 draw on the south coast, but he claims that he is used to having to fight for his job.
"My whole football life is pressure, if I don't get pressure from outside I put pressure on myself," he told Sky Sports News. "At least we got one point, I think a point well deserved. We were the better team, most of the time we had good ball possession - maybe we had to create a bit more.
"After 1-0 we showed character and finally maybe had to win the game in the last few seconds. We are in a difficult situation but it's one thing to come out of this and show fight like we did today.
"The first goal we are not really attending to the situation. You need to stay on your feet in the situation of Dominic [Calvert-Lewin] and [Morgan] Schneiderlin."
Everton, who spent close to £150m on strengthening their squad in the summer, are three points above the relegation zone after eight games.