The Hammers goalkeeper was on top form, making a number of important saves but the visitors failed to find the net at St Mary's 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."
West Ham manager Sam Allardyce also bemoaned his side's inability to score with James Collins blazing a good chance over late on.
He told Sky Sports 1: "We could have won it at the end when the chance he had was probably our best chance of the game, unfortunately for him it's fell to the centre half.
"At the end of the day that far out he should at least hit the target but overall (it was) a decent performance.
"Defensively we showed how good we are, I think we have only conceded one goal in four games, but we just can't find the back of the net.
"Three games without a goal is my concern - it's not as if we haven't created any chances or good opportunities in and around the final third today to try and score but it's just eluding us at the moment.
"When a golden chance falls that late in the game you want to put it in and walk away with all three points."
Allardyce made no bones about the fact he believed Saints midfielder Morgan Schneiderlin should have been sent off for a challenge on Mohamed Diame.
The former Bolton boss said: "We feel a bit disappointed that Schneiderlin is still on the pitch - we didn't even get a free kick - because it's a two-footed challenge.
"(With) two-footed challenges, we have been told by everyone in the referees' department from Mike Riley down, there is no other choice but a straight red - this one we didn't even get a free kick.
"I can't for the life of me (understand) - Andre (Marriner) is such an experienced referee now, how he didn't see that.
"For me that was a disappointment. It's in the end kept them with 11 men on the field which the law was supposed to be they should only have had 10 men which would have given us a better chance of winning.
"But I'm happy with a point. I can't affect what the referees do, it's not my job."
Schneiderlin felt he had not committed a poor challenge, saying: "I need to see the image again but at that moment I didn't think I had done anything wrong.
"I didn't have the feeling at the time that it was bad, I am not a player who commits those kind of fouls.
"If I touched him in any way I apologise but I have not the feeling that I did anything wrong."
Of the result, the Frenchman was disappointed, saying: "We had three or four very clear chances and their goalkeeper made some very good saves.
"It is very hard to take because we had the feeling that we did everything to win that game.
"Now it is up to us. Next week we have a very hard game at Anfield so hopefully we can improve this week and score some goals."