TC, now retired from the game, was a keen spectator at Elland Road in his role as a co-commentator and summariser for Sky Sports, and insists that the team must now look forward rather than dwell on where it all went wrong against David O'Leary's men.
Says Tony: "It was a disappointing result but, to be honest, the game was lost in the first six or seven minutes with Leeds scoring twice.
"It's easy to criticise players, but sometimes you have to sit back and accept that the better team won on the night. Leeds played very well and I don't think anybody would have beaten them on that particular occasion.
"West Ham actually settled down well after the two goals and played some nice football but the third goal killed them off. It was a fantastic finish from Robbie Fowler and there was no way back after that.
"The important thing is that people don't get too carried away with the defeat. The team have been playing very well recently and Glenn and the players can take heart from some of the results they have earned against the likes of Manchester United, Arsenal and Liverpool.
"Most people wouldn't have given West Ham much of a chance when looking at those games but they have secured an excellent number of points and there is certainly no need to panic after losing to a very good Leeds side.
"Now they've just got to put it behind them and look to get back to winning ways in the FA Cup on Sunday."
Tony, who scored 12 goals in 29 FA Cup appearances for the Hammers - the last of which was scored against third division Wycombe Wanderers in January 1995 - admits that north west minnows Macclesfield won't go down without a fight.
"It won't be an easy game and Glenn will know that - he certainly won't be taking anything for granted.
"The fact that BBC have chosen it as the live game proves that they see it as a possible upset and I am sure that the players will want to prove otherwise.
"They have got to do a professional job and just make sure they get through to the next round. If that means settling for a scrappy 0-0 draw and completing the job in a replay at Upton Park, then so be it."
Looking back over the season so far, Tony, who has been present at every home game now that he is a host in one of the executive lounges in the Dr Martens Stand, feels that Glenn Roeder deserves recognition for his achievements so far.
"It was always going to take a while for Glenn to get his ideas and methods across but I think he can be proud of the job he has done so far.
"Forgetting the major defeats at Everton and Blackburn, the form has been pretty good and there have been some fantastic results against the top sides.
"Bearing in mind the turmoil caused by Harry's departure last season and the fact that many critics were tipping the side for relegation this year, things are going well and the club is definitely heading in the right direction again.
"If the team can hit a real good run of form now, anything can happen, because the league is very close and finishing in 7th or 8th place may be enough to secure a UEFA Cup place.
"There are games coming up against the likes of Leicester, Southampton and Blackburn - games they should be aiming to win - and there is certainly reason to be optimistic now."
The mood will certainly be bubbling if the Hammers can begin a march to the Millennium Stadium in Cardiff and Cottee is one of thousands of lifelong supporters who are still dreaming about a long-awaited FA Cup triumph.
"A cup run would be nice - it is certainly overdue. It's been 22 years since we last won a trophy and that is far too long for West Ham fans."