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.
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."
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