Eden Hazard headed Chelsea into a seventh-minute lead at Stamford Bridge, but it was not until after Tom Huddlestone was shown a 60th-minute red card for a challenge on Filipe Luis that the hosts were able to add to their tally - Diego Costa diverting the ball beyond goalkeeper Allan McGregor.
In addition to the sending off, Hull boss Steve Bruce felt aggrieved that the already-booked Cahill escaped further punishment for an alleged dive in the Hull penalty area before Huddlestone saw red.
But Mourinho insisted it is not in Cahill's nature to attempt to deceive the referee.
"I didn't see it on TV and I was very, very far away," he said. "But I don't believe Cahill dived.
"If you tell me I'm wrong [and that] he dived - something happened, or they blocked his run, or he got a touch, or he lost his balance.
"But that big honest guy? I don't believe he dived in the opposition box."
Chelsea looked set to go on and register a thumping win when Hazard capped an early period of dominance with a goal.
That early promise fizzled out, but the victory still rarely looked in doubt for the home side.
"We didn't play especially well, but we played well enough for everybody connected with Chelsea to be calm," Mourinho continued. "It was always under control. We never felt really that the game was at risk.
"Today we just had moments of good football, moments of happiness and creativity, but just moments - not for 90 minutes.
"It was a good enough performance to win against a difficult team, which was important."
Mourinho and Bruce appeared deep in conversation for long periods of the match, and the Chelsea boss revealed the pair have a good relationship.
"With some [managers] I cannot say goodbye five seconds before the end of the game, with others I can speak all the game," he added. "Two old foxes, no pressure, just enjoying.
"He's a great guy, Steve."
