Fans chanted for Zola's dismissal during the match, and afterwards striker Carlton Cole was involved in an altercation with one such disgruntled supporter following what was a fifth straight defeat.
Related ArticlesPremier League relegationCarlton Cole clashes with fanZola: West Ham fans should pick on me not playersWest Ham 1 Wolves 3West Ham v Wolves: match previewZola stays calm for West HamChants of "You're not fit to wear the shirt" also rang out around the Boleyn Ground, and England defender Upson appreciates efforts have just not been acceptable of late.
"We are in a position where, certainly at home in the last couple of games, we have not delivered performances that were acceptable," Upson said.
"At this stage of the season, looking at our league position, you could say we are close to that point [rock bottom] and perhaps we need to realise that before we can make forward steps.
"It is not a nice feeling, but what we are going to do about it is what we need to be focusing on and there are enough games left for us to accumulate the points we need.
"We need to have a long, hard look and change something about what we are doing.
"It is up to us, the management and the players, to do something."
Upson added: "It just looks like we have lost that ability to work as a team at the moment.
"We need to go back to basics on that front and realise what we've got to do tactically to get the three points.
"We need to work on that on the training pitch, and probably off it as well, and be more of a group. Hopefully, that will change our performance against Stoke for Saturday."
Upson understands why some supporters vented their frustrations so publicly.
He said: "It is because the supporters are passionate and it works both ways - we are worshipped when it is going great and when it is not, you're at the other end of the stick.
"That is part of the game and part of the pressure of playing for a club like West Ham.
"The expectation is high and, when it is not delivered, you get told about it.
"I like that, personally, and I would rather have that than play at a club where people are not too bothered.
"Is it helpful? Probably not at this time, but it is a test of us as a team - and if you can't deliver then you should not play for West Ham."