Rangers boss Neil Warnock had promised his players early in the season he would continue to wear shorts until they lost their first league game.
"Thank God - I can have my long johns under my tracksuit now for the winter," said Warnock.
"It was obviously disappointing. But if you'd told me we'd have got to December unbeaten I wouldn't have believed you."
Warnock felt his side should have had a penalty before Watford took the lead, John Eustace appearing to handle in the area.
"For the handball, the referee was in a great position but Eustace has been too clever," added Warnock.
"Then we are losing 2-0, we regrouped at half-time and changed a few things and we get an offside like that!
"But all credit to Watford - we could have been beaten by 10. We'll have to take it on the chin.
"The players have got their Christmas party tomorrow. I told them not to think about tonight but to take the league table with them instead."
Rangers, who pulled one back through Tommy Smith, could find themselves in hot water after Watford midfielder Stephen McGinn appeared to be hit by a bottle thrown from the crowd after Mutch curled in their second goal.
"I'm not sure what happened but Stephen has a large cut, his eye is closed and he's got concussion," said Hornets manager Malky Mackay.
"The fourth official told me three bottles of beer were thrown from the top tier."
But Mackay did not want the incident to overshadow a fine win.
"I'm delighted with way we played," he added.
"We came up against the league leaders who have an experienced manager and experienced players, and they are a team I think will be promoted.
"There was an unbeaten record, it was live on TV and a great atmosphere... it was a game I'd loved to have been playing in and I'm very proud of my players.
"On another day we could have had a few more goals."