Matthew was given the supporters' award before the win over Watford on Saturday and Tony says:
"I thought it would be Matt and as well as being Hammer of the year I think he has been most improved player of the year as well.
"He has got better as the season has gone on, and I think that really is the test of a good player - he has done it this season.
"I saw him on a couple of occasions for Spurs but he couldn't really break in on a regular basis.
"I did think at the time that he was a little bit weak then and the thing that you need is a little bit of belief in yourself - Glenn Roeder gave him a little bit of that and then Alan kept him in the side."
Tony sees a stronger player now and adds:
"Physically, in the Premiership, that side of it can hit you.
"I don't mean that it is not physical in the first division because there are more tackles flying in and you can get away with a few more than can you can in the top flight.
"But, in the Premiership, when you are shoulder to shoulder with players in one on ones I didn't think Matt looked like he was going to go past anyone.
"This year he has gained a bit of confidence and strength and he has looked like he is always going to get a cross in when he is on that left hand side.
"Whenever he hasn't been in the side it has shown you even more what a good player he is because we have missed him ever so much.
"He does give you that all-important balance on the left hand side.
"He is a good player and let's hope he is showing it in the Premiership next season; that will be a step up, I have got to be honest, and that will be another thing for Matt to prove.
"He has proven himself in the first division; last season he didn't have the best of seasons, but no one did - it was a struggle all round and I don't think that can just be labelled at him because it is very difficult to play in a side that is not doing well.
"In the Premiership he will have it to prove - as will all the players.
"It is a great honour and if he just has a look at that trophy - and I didn't win it in the 10 years I was there - there are some great names on it and he should be a very proud boy."
Runner-up was Michael Carrick, and Tony adds:
"I think Michael may have found it hard to adjust to the first division and to the fact that a lot of his friends have left the club - but for me this boy has true quality and could play for a top three side.
"If he did leave West Ham - which I hope he doesn't - I would like to see him playing for Arsenal because he is that good.
"But hopefully he can get us into the Premiership - though it may be difficult to keep him if we didn't go up this season.
"I would like to see him sign on the dotted line like Anton has just done - we need to keep our class players and I think Michael is probably the best player on the books."