"They have got to keep it going because, although we were looking at 36 or 37 points being safe, I can realistically look at that target now and say it is going to be over 40," he says.
It wasn't too long ago that most pundits were predicting three from the bottom four to go down, with many feeling it was a straight fight between the Hammers and Bolton for the first safety position.
But Tony says: "The way Bolton and West Ham are playing I think there are going to be more wins on the horizon, so it is going to really up the ante with the other clubs as well."
Bolton fielded an all-foreign side for the first time in their history when they beat Tottenham recently, and Tony adds: "It was a big blow Bolton beating Spurs last week and I could have killed Gary Doherty for giving that penalty away in the last minute.
"It was funny to be sitting at home supporting Spurs and thinking about what they had to do - a strange situation.
"But, although it came late, Bolton deserved the win. Now I hope all the rest get dragged in."
Of 'the rest', while Fulham and Manchester City are not mathematically safe as yet, they can consider themselves very close indeed, while Birmingham City, who spent a lot in January, have coped well with injuries - although they won't have Clinton Morrison to call upon this season.
Which leaves Aston Villa, whose top scorer Dion Dublin is suspended for the trip to Upton Park a week on Saturday, and Leeds United, who have beaten West Ham twice this season.
"Aston Villa have got a terrible run-in and of course one of those games is against us at Upton Park," says Tony, "so if we can beat them there, and with some of the top teams Aston Villa have got to face, sometimes when you get dragged into it at the last stage that is when you get a bit twitchy and a few bottles start to go.
"Hopefully West Ham get a result at Southampton who we hope will have an eye on the FA Cup semi-final, and I can see Charlton beating Leeds in their next fixture, which would only put us a point behind Leeds.
"It doesn't matter what kind of run-in you have then, you still have to get the points, and if you are on a roll, as West Ham are at the moment, or on a dip as Leeds are, I know who I would rather be."
Although Leeds have lost their last four games, and seven out of their last nine, with four home games remaining they are hopeful they can pick up the points to keep them up, and earn Peter Reid a few bob in the process.
But Tony is banking on West Ham's new found strength in depth to see them through, and the return of Paolo Di Canio into the fold after another hard fortnight's training, including a spell in Bologna.
Tony says he could help provide the inspiration, explaining: "He wasn't on the bench against Sunderland but certainly, in the game at Southampton, if he is not in the side I would like to see him on the bench - because he can turn a game around on its head.
"If there are 20 or 25 minutes to go and there is a little bit to be done, there is a certain genius you can bring off the bench.
"He can save the club by coming on as sub, and many a great player has come off the bench to turn a game."
Adding his own - strictly personal - views of who might be involved at the weekend, he says: "If you look at the way Fredi finished the second half against Sunderland I think Fredi will come back into the starting line-up with Lee Bowyer probably coming in for Stevie Lomas on the right hand side, because he is more natural in that position - and I don't think you can afford to drop Joe or Michael at the moment the way they are playing in the middle.
"It is hard on whoever gets dropped but I think you have to realise that at this stage of the season it doesn't matter about your own personal pride - it is all about the club now and trying to survive.
"Those on the bench will still have a big role to play."
As for the non-inclusion of Jermain Defoe and Joe Cole in the full England squad, he reckons: "Jermain's form and Joe's form have come a bit late in the season, since he was switched to the middle, but I think if they look at it realistically they can't say they have had a great season to force their way into the full side.
"The pair are excellent players and Jermain in particular in the last couple of weeks has really grown up.
"The fact that he has got a regular partner alongside him has, I think, really made the difference, when a lot of the time he has been trying to run the line on his own - which is very difficult."