looking for advice

[KHanneman]

Was working a travel 15 game, my last game of 7 for the tournament, and I'm thinking how good of a job I'm doing so far in the tourney (my fourth year umping). This was pretty good baseball, anways, I'm PU and the visitors are up to bat in the last inning, down by 5 runs, runner on 3rd, 2 outs and the count is 3-0. Next two pitches I call strikes and the head coach goes bezerk. Walking all the way down from the 3rd base coaches box, screaming- and I mean screaming- about the last two strike calls. I call time, take off my mask and take a couple of steps so we are face to face and calmly tell him he can't argue balls and strikes. Still screaming- he says he's not arguing balls and strikes, the freaking (yeah, said freaking instead of fu**ing) ball was in the dirt. I look at him without saying anything else, and he turns around to walk back to the coaches box, still complaining about the calls. The runner ends up walking, the next batter strikes out swinging and game over.
My question, should I have ejected the guy, which I didn't because it was toward the end of game, he may have had a point (my partner didn't offer any help postgame as to whether the pitches were clearly balls), and I didn't want the coach to have to sit out the next game of the tourney.
Looking for experienced guys to guide me here.
Thanks.