Hughes and Al Mubarak held talks before Sunday's game to discuss the long-term plans for the club, with the manager expected to fly out to Abu Dhabi to discuss his list of targets at least once ahead of the January transfer window.
Al Mubarak added: "Thankfully I do not read the newspapers that are saying Mark is under pressure but I find it incredible.
"I am told that there are reports that we are associated with two different coaches and that we are about to sign them. It is rubbish.
"This is a winning team that is going through a learning curve right now.
"While January is going to be an interesting opportunity for Mark to improve the team, this is an exciting dynasty we are building and we are only in the first two months.
"I think people will see then that we have good foundations in place in the team, we have a good coach and that we will be upgrading in terms of players. Hopefully the results will come."
I am told that there are reports that we are associated with two different coaches and that we are about to sign them. It is rubbish
Khaldoon Al Mubarak
Hughes, who took over from Sven-Goran Eriksson at Eastlands in the summer, has seen his team register four wins and seven defeats in the Premier League this season, despite the signing of �32.5m Brazilian superstar Robinho.
The club's poor form has generated speculation that new owners the Abu Dhabi United Group, who are backed by Sheikh Mansour Bin Zayed Al Nahyan and bring unrivalled spending power to the top flight, may lose patience with the team's inability to find consistency on the pitch.
The group bought City from UK Sports Investments Ltd, which was led by former Thai prime minister Thaksin Shinawatra.
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