Full-back Jack Grimmer netted the decisive goal after assisting his side's first strike, as the League Two side marched into the FA Cup fourth round impressively.
"It's clearly a difficult time for us," Stoke manager Hughes told reporters. "When we make mistakes, they're getting penalised. We're not giving ourselves the right defensive platform at the moment and when that happens you're always vulnerable.
"Clearly, the only way to quieten down the noise around the club is to win games. We need to turn it around and quickly. We're good enough in this league - we've proved it during my tenure - but we've got to be better in key moments.
"Credit to Coventry. They deserved the win for defending manfully and putting bodies on the line. I wish them well."
Stoke will be looking to right their recent Premier League woes in their next game, which is a trip to Old Trafford to face Manchester United.