The Grecians had not won in front of their own supporters since November 6 and went into the game with only three victories on home soil all season.
But a John O'Flynn double sandwiched Scot Bennett's superb header as Exeter picked up three big points to move into the automatic promotion places.
Sturrock said: "We are very disappointed. I thought we had a lot of opportunities in the box and we didn't get on the end of them. We lost a bad goal two minutes before half-time and if we had scored first it might have been a completely different game.
"The second half was a weary-looking team trying to chase the game and it has cost us dear.
"I thought we got into the right areas in the first half but our final finish let us down.
"We have lost three league games in a row now and we need to focus on that because we haven't scored a goal in that period either. For the team performances we have put forward this season it is not good enough and I will have to look into it."
Sturrock added: "There are two or three positions we need to strengthen. I am looking at the squad and it is threadbare.
"I have got three weeks in January to bring in some players. Anybody coming in will be cup-tied but we can still hopefully bring in players that can help us in the league."