Christian Benteke's injury-time goal snatched a 2-1 victory for Hodgson's Palace side even though they had spent much of the game defending but the coach argued that taking chances is what matters in football.
Hodgson said: "The game's about scoring goals and not letting any in.
"I thought we worked unbelievably hard to try and make certain we didn't let any goals in.
"I thought we worked so very hard to stop them getting many chances and tonight we were fortunate that the couple of chances we did create - and they were both very good goals - we took.
"The statistic that counts at the end of the day is goals against and goals for.
"Okay, they had the better of possession, that's for sure, they had the ball in our box more often, they had more quality but I'm not going to apologise for coming away with what we consider to be a very good victory."
Poor recent results had sparked unrest amongst Palace supporters but Hodgson insisted that he did not feel "vindication" after the late win.
He said: "I don't feel the need to be vindicated. I don't like to use that word because the use of the word vindication would suggest that something has been going awfully wrong in what we have been trying to do for the whole of the season. I don't think vindication is the right word."