West Ham apologise to fans after FA Cup rout at West Brom
The visitors conceded two goals in each half and finished with 10 men after substitute Morgan Amalfitano was sent off after 70 minutes.
Gold tweeted: "I feel sorry for myself but most of all I feel sorry for the thousands of travelling West Ham fans."
Adrian called the result "shameful" as West Brom eased into the last eight.
The Spaniard, able to play after his red card from a sending off against Southampton in mid-week was over-turned, added via Twitter: "After this shameful result in FA Cup, just we can say SORRY to all West Ham fans! Now we need to be united and fight in Premier League."
West Ham are eighth in the Premier League table and lost for only the second time in 10 games.
Manager Sam Allardyce claimed draws against Manchester United and Southampton - when they effectively ended the match with nine men duo to Adrian's dismissal and an injury to Andy Carroll - in the previous six days had taken their toll on his side.
Allardyce said: "I would say it (the defeat) was probably coming based on what we've had to cope with over the last few weeks and I think it told on us, there's no doubt about that.
"I have to give West Brom a lot of credit - they were very good. But I look at the players and there was not the energy we know they've got based on all they've done in the last few weeks."
Amalfitano was sent off after pushing Chris Brunt in the face, moments after being booked for kicking the West Brom defender.
Allardyce added: "It's unprofessional, isn't it? That will be dealt with, as always, internally and we'll move on.
"But I don't think it's made any difference to the result."