Gold says the club can also be proud with the number of former Hammers in the squad.
"I am thrilled for Robert and Matthew," he told whufc.com. "They are two great ambassadors for the club in the true West Ham spirit and indeed for England. They are proper gentlemen and conduct themselves well on and off the pitch."
While eight others in Capello's squad have West Ham connections - captain Rio Ferdinand, David James, Glen Johnson, John Terry, Michael Carrick, Frank Lampard, Joe Cole and Jermain Defoe - the chairman was disappointed that Scott Parker and Carlton Cole both had to stay behind.
"I am sorry for Scott that he missed out in the end. I just wished we could have had three players at the finals so that we could have emulated the 1966 ideal with Bobby Moore, Martin Peters and Geoff Hurst lifting the trophy.
"I can only say to Scott that if I was the England manager I would have taken him. He should take it as a positive that he got so close. We have seen him week in and week out and we know what a player he is. They talk about players that turn matches and Scott Parker is one of those players.
"You could say the same for Carlton as well. While I am disappointed for both of them, the upside is that they will be stronger and more resilient to our new season which is going to be very important. It is the beginning of a new era at West Ham United."