The Hammers goalkeeper was on top form, making a number of important saves, but the visitors failed to find the net for the third consecutive match.
They have scored two goals in four games this season, although they are without the injured Andy Carroll while Croatia international Mladen Petric is not yet match fit.
On whether he was worried about their lack of cutting edge, Jaaskelainen told Sky Sports 1: "A little bit but we are creating chances, we just have to start putting them away."
He added: "The clean sheet gives me most satisfaction. We worked hard...and we had a couple of chances to get a goal."
Midfielder Mark Noble paid tribute to his team-mate, saying: "He was brilliant, when you clean sheets it's a massive help. We are not scoring goals but we are keeping clean sheets.
"I thought it (the result) was quite fair. We're happy with the point. The lads dug in well."
However, Noble admitted he wanted all three points before the match, saying: "We came here to win the game. We could have nicked it in the end and then everyone would have said it was a smash and grab.
"Southampton played well and Jussi made a couple of good saves."