The Tech 3 Yamaha rider was on course for a career-best result when he crashed out eight laps from the finish of the wet-dry race.
The injury did not prevent Crutchlow from returning to the track for Wednesday's post-season test day at the same venue.
He was relieved that the weather cleared in time for him to get some laps in at the test to assess the injury.
"I'm happy because I could check my left hand that I injured in the race," said Crutchlow.
"I have a small fracture on an old injury but it didn't feel too bad."
The Briton was second fastest behind Dani Pedrosa's Honda at the test.
Tech 3 team boss Herve Poncharal said he was glad Crutchlow got the chance to show his pace on Wednesday after the blow of Sunday's crash.
"It was good for him to do a few laps and get his confidence back after the crash on Sunday," said Poncharal.
Crutchlow agreed that Wednesday's time had helped him get the accident out of his head.
"I didn't want my last memory of 2012 to be crashing out of second in the race on Sunday, so now I can go into the winter in a positive frame of mind," he said.