The Cottagers won the game 1-0 thanks to a goal from Jonathan Greening 16 minutes from time.
Hodgson told Sky Sports: “Tonight’s victory was a crucial one for us, it was a little bit of a make-or-break.
“If you go to a sixth defeat at home to Portsmouth it’s hard to get your season back on track.
“To win was the all-important thing. I’ve seen us play better, but I’ve seen us play better and take nothing so I will be quite happy and be grateful for the three points.
“I’ve got to say it was a fairly fortunate victory, but I think I can put that into context with all the rather unfortunate defeats we’ve had lately where we haven’t really deserved the results we’ve got. It was good to get the three points and get over the 30 mark.
“It was a good performance from Portsmouth and I can imagine Avram Grant must be absolutely devastated not to get anything from the game but I know how he feels because I have been in that position once or twice myself recently.”
