Moyes felt his side had been denied two valuable points that seemed certain after two late goals by Marko Arnautovic.
West Ham are allowing Collins, 34, to talk to other clubs in the final year of his contract.
However even the most hated referee ever to officiate a game involving West Ham agreed that Bobby Madley made a complete howler of yesterday's match against Bournemouth, which ended 3-3 after the 32-year-old Yorkshireman overruled his linesman in the most dubious and unique circumstances in order to award the CHerries an added-on time equaliser. It is disappointing not to take three points as we played well until the slip. The worst part is that it's a Bournemouth player who puts the ball in the net with the top of his arm.
Goals from Dan Gosling and Nathan Ake had put Bournemouth ahead after James Collins had headed the visitors in front.
I think Madley was trying to be too clever by ignoring his assistant and he has to show trust in his colleague. "We entertained everybody this Boxing Day and I hope people enjoyed the match, but I would have enjoyed it more if we had won".
'The decision (over offside) was tight, but I thought once the flag had gone up that it wouldn't be given, especially because of the length of the conversation they had'.
All Whites captain Winston Reid was relegated to the bench as West Ham fought to a 3-3 English Premier League (EPL) draw against Bournemouth on Wednesday morning (NZ time).
"We have to get back on the training ground and see if we can work on a lot of things", he said.