The Hammers, down to 10 men after Marko Arnautovic's early red card, twice came from behind in their Premier League fixture at St Mary's Stadium.
Bilic told reporters after the game: "We are very disappointed we lost a point but we gained a lot of things.
"We showed character, quality and that we can cope with 10 men and we can score two goals and we can stop them scoring. We had two or three chances to take the lead. It is a disappointing way to lose he game.
"There is no point talking about the penalty. I am proud of my team and they showed everything I asked. Commitment, quality, character, team spirit and we never gave up."
West Ham are in EFL Cup action on Wednesday at League Two side Cheltenham Town before travelling to Newcastle United on Saturday.