"It has been a tough old season - unexpectedly, really, because I didn't think we would be in this sort of trouble after finishing seventh last year," says the former Hammers boss.
"I thought we would be in for another decent year and maybe some cup runs, but it has been disappointing.
"I have seen them recently and there is certainly a lack of confidence, but Manchester United in the FA Cup was the first game where they looked like they have packed in.
"It was a very poor performance and I have known people that have supported the club for 40-odd years and they said that was probably the lowest point in the club's history - that is how bad they thought it was.
"But they bounced back against Blackburn before the disappointing defeat at home to Liverpool and I think the fans have been terrific.
"You sense there was a togetherness about it against Blackburn with the fans really wanting it; they stuck with them and it ended the right way.
"You can see the confidence flow away if they don't get the early goal and of course bad goals have been going in from a defensive point of view.
"I think it is a bit fragile at the back confidence-wise and in midfield with the ball being given away, but you expect that on the run they have been on - you are going to get that edginess."
Despite that analysis, Billy is optimistic about the immediate future, and he adds: "The beauty of it is now is that Glenn Roeder has got options on the bench whereas in the last few weeks you have had kids on there.
"They will always cause problems going forward, it is just defensively where they have struggled.
"The board have stuck with him and I would be pleased if he does turn it round - I know what he is going through.
"I had one year of it when we had the Bond scheme. We were middle of the table in mid-November when it came out, we had just beaten Arsenal 1-0 and drawn with Liverpool 0-0 on the box when we should have won, and after that we didn't win a game.
"It was horrible and when everything is going against you it can be very lonely. I know what he is going through.
"Nobody wants to see him get the sack and I was delighted they got that first home win last week - but they have still got it all to do.
"Glenn is not a fool and he knows when you are on a run of one win in 17 games your job is on the line every week - and it has been like that for the last couple of months for him.
"I have no doubt the board have sat behind a closed door somewhere and weighed up their options but they have decided to stay with Glenn and let's hope they are justified.
"I want the club to stay up, obviously, but if Glenn stays that would be good for everybody.
"I think Glenn will keep them up and I have said that all along.
"The thing is, they are four points adrift of Bolton and with the run they have been on it could have been 10 points adrift which would have been a mountain to climb.
"But four isn't a lot to make up because with one win you are just a point behind.
"West Ham have got better players than West Brom, Bolton, and Sunderland so I don't see where those teams are going to score many goals from - whereas West Ham have got goals in them now, and they have the better quality players.
"If everyone pulls together they can get out of it, and when you are at any football club in trouble, it is important everyone does that - the board, the manager, and above all the players.
"They have to realise just how serious it could be if the club did go down, and they have to do the business for the club in the last 12 games, which will be real cup tie stuff."