"That's great," Matt says ... "Good for him. He deserves it!"

Of course ... Mookie went head-to-head with Trout and the Indians' Jose Ramirez for the award -- but dominated the voting thoroughly, winning in a near-unanimous decision.

Damon tells TMZ Sports that's the way it shoulda been ... and he ain't wrong -- Betts batted .346 this season with 32 home runs and 30 stolen bases.

BTW ... it's not like Mookie was in much need of the confidence booster -- dude just won the World Series, had a new baby girl AND nabbed a Silver Slugger Award last week.