Ayegbeni missed a series of good chances before finally finding the net in the 68th minute.
Sturrock said: "I'm very upset for the fans because there was only one team trying to win the game.
"We have got to start thinking about our mental approach to matches. Local derbies are cup finals and there was only one team who treated it as a cup final, where as we just played it like a normal league game.
"A lot of my players just got through the 90 minutes and some of them are going to have to make changes if they are to become a regular in my team.
"That's two games I've been in charge in which our main aim has been to stop the other side playing. We need to start realising that we need to try and win the game as well.
Ayegbeni should have had two goals in as many minutes in the first half.
The Nigerian scuffed badly wide after being played through by strike partner Teddy Sheringham on 16 minutes and should have done better after racing on to a Steve Stone pass soon after. But instead he fired harmlessly wide of the left post with only Antti Niemi to beat.
However, Ayegbeni made amends 23 minutes into the second half when he tapped home from four yards out after Stone had crossed from the right.
Delighted Pompey boss Harry Redknapp said: "That was a big win because it was a local derby, but also because we needed the points.
"Beating Southampton was something extra for the fans and I'm sure it will give everyone a lift."