I think Belichick may have liked the odds of missing a FG attempt from at least 45+ (ended up being 48) more than the idea of spending the timeouts and allowing them to convert and run the clock down.
That's my guess, anyway.
I'll post each play and my thoughts at the end.
Panthers 32 yard line/ 2:13 : 1st and 10 - Stewart runs for a first down. Panthers let the clock run to the two minute warning.
Panthers 47 yard line/ 2:00 : 1st and 10 - Incomplete pass to Funchess. Butler almost intercepted.
Panthers 47 yard line/ 1:53 : 2nd and 10: Newton runs up the middle for 7 yards
Patriots 46 yard line / 1:04 : 3rd and 3 : Funchess first down.
Patriots 41 yard line / 0:46 : 1st and 10 : Stewart run up the middle. Ridiculous Holding penalty on Chung. Automatic 1st down.
Patriots 34 yard line / 0:40 : 1st and 10 : Cam up the middle to the 31.
Patriots 31 yard line / 0:18: 2nd and 7 : Cam up the middle to the 31.
Patriots 30 yard line / 0:04 : 3rd and 7: Field Goal.
Where do you use the timeouts? My guess is that the stupid holding penalty called on Chung threw a wrench into whatever plans they may have had.
I guess you could argue that they could have used their timeouts during the last series to give TB some time but they, because of the fraudulent penalty, were already in field goal range.
So I'm not sure when would have been the best time to use them.