Allardyce has been heavily scrutinised recently after a run of results which had seen West Ham win just once in their last seven Premier League matches before the victory at the Cardiff City Stadium.
But Gold said the 59-year-old's position had never been under threat as far as the board were concerned, insisting Allardyce should not be blamed for factors beyond his control such as the injuries to a number of key players.
"People talk about the dreaded vote of confidence but what we say is what we mean," Gold told Sky Sports News. "Sam has done everything we've asked of him.
"Our view is that Sam was doing nothing wrong other than that he had an injury list which was pretty devastating but you can't blame him for that."
Asked if he and co-chairman David Sullivan would back Allardyce till the end of the season come what may, Gold said: "Well you know that. We've gone public - Sam Allardyce is our manager."
Sullivan added: "If you were looking for a manager to keep you up you'd be looking to appoint Sam.
"But we've got a long way to go. He knows it, we know it and the players know it.
"We've given away too many points and made too many mistakes but we've put ourselves back in with a fighting chance (of avoiding relegation)."