But Hughes insists the Portuguese is the man to turn Chelsea's fortunes around.
"We are all been in that situation, you just have to keep winning so the focus goes elsewhere," Hughes told the BBC.
Mourinho 'gives up' on stadium ban appeal
"I have had similar situations and sometimes you go under.
"Jose Mourinho has enormous credit at Chelsea, he has delivered trophies and surely people should cut him a little bit of slack.
"I see no reason why they should make a change but there is always focus in the Premier League."
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Chelsea have never lost three straight league games under owner Roman Abramovich and there are calls for Mourinho to get the boot.
The upcoming international break means Mourinho has two weeks to source Chelsea's problems before they Norwich at home.
Stoke, meanwhile, move up to 12th in the league.
"We displayed great character today, all the qualities you need to compete against one of the best teams in Europe. They have world class players," Hughes added.