Chief executive Richard Bevan accused the Abu Dhabi-owned club of changing the goalposts for Hughes, who was replaced by Italian Roberto Mancini within minutes of Saturday's 4-3 home win over Sunderland, and warned of further sackings elsewhere.
Big-spending City, the world's richest club, are sixth in the Premier League and have lost just twice this season while also winning only two of their last 11 league games.
"I spoke to Mark last night and he found out immediately after the game when he was called into a meeting and informed that his contract was being terminated," Bevan told BBC radio.
"But I think the decision had probably been taken some time ago.
"He knew that there were key goals he had to hit and his target was the top six. He was very disappointed because they were on target for that ... to me it looks like the goalposts were moved.
"I think owners must realise, particularly overseas owners, that they can't just buy trophies in one season," he continued.
"If they feel that, then we will continue with the sackings and we will continue with affinity lost to our clubs in England. I'm pretty sure the Manchester City fans will be very sad to see Mark go.
"If you come in as an overseas owner, you need to embrace the city, the supporters and not just the trophy cabinet," said Bevan.
Sunday newspapers reported that a group of players led by Irish goalkeeper Shay Given had tried to confront City chairman Khaldoon Al Mubarak over the decision after the match.
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Hughes was the Premier League's second managerial casualty of the season after Portsmouth's Paul Hart was sacked by that struggling club's Middle Eastern owners.
Hart has since joined Championship Queens Park Rangers, whose owners include Italian former Renault F1 team boss Flavio Briatore. They have now had 11 full-time or temporary managers since 2006.
Tottenham Hotspur boss Harry Redknapp felt Hughes had not been given enough time.
"I couldn't believe it really, I'm disappointed," he told the BBC.
"Two defeats is certainly not a disaster and they've got a game in hand and were sitting just off the European places. I'm surprised that they have taken that decision at this stage in the season.
"Mark's a good manager and given time there's no doubt that they would have been very successful."
Half of England's 20 Premier League clubs have foreign owners and Redknapp said the landscape had changed.
"It is different now," he said. "You have got multi, multi-millionaire owners who all want to be number one.
"In their lives they have made so much money and they do what they want with their lives, they are so rich, and they all expect to win.
"The more that come in, the more you are going to see managers come and go. The merry-go-round will be even worse because they will all be disappointed they are not top of the league. They won't understand it."
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