Red Sox first baseman Kevin Youkilis wasn't too pleased, either, and TV replays seemed to support his beef.
Howard Kendrick was at the center of two of the calls in question.
As it turned out, the calls didn't factor into the outcome as the Angels claimed a 5-0 victory.
"I thought they both were outs, CB disagreed, so you just move on and go from there," Youkilis said. "It's not a big deal after the game. It had nothing to do with us losing. I'm not really worried about it."
With two outs in the fourth inning, Kendrick slapped a grounder up the middle. Red Sox shortstop Alex Gonzalez, making a nifty sliding stab, came up with the ball. Gonzalez set but threw wide to first, pulling Youkilis off the bag.
Youkilis made a swipe tag on Kendrick, who was ruled safe at first base. Immediately, Boston manager Terry Francona trotted out to protest. TV replays seemed to support the argument that Kendrick was tagged before touching first.
"[Bucknor] said I tagged him, but he was on the base when I tagged him," Youkilis said. "I didn't think that was possible."
The play didn't cost the Red Sox a run, however, as Jon Lester struck out Jeff Mathis to end the inning.
In the fifth inning, there was a disputed play at first, and this time Angels manager Mike Scioscia raced from the dugout to have a few words for Bucknor. The play that triggered the argument was Chone Figgins' sacrifice bunt after Erick Aybar doubled to open the inning.
Figgins' bunt was handled by Lester, who threw wide to second baseman Dustin Pedroia covering first. Pedroia came off the bag to catch the ball. But he lunged back with his left foot reaching the bag about the same time as Figgins. On a bang-bang play, Figgins was ruled out. Disagreeing, Scioscia had a few words with Bucknor, who appeared to have got the call right.
"I couldn't tell. I haven't had a chance to look but it was close," Figgins said. "I couldn't tell."
The sacrifice bunt set the stage for Torii Hunter's three-run homer off Lester.
The controversy continued in the sixth inning when Kendrick bounced a grounder to Mike Lowell at third base. But Lowell's throw caused Youkilis to jump. Making a terrific recovery, Youkilis got his foot down on the bag. But Bucknor called Kendrick safe.
Again, Francona was out of the dugout and exchanged some more words with Bucknor. The play didn't cost the Red Sox any runs because Jacoby Ellsbury made a sparkling running and diving catch to pull in Figgins long fly ball to center field.
Afterward, Lester noted the human element impacts the umpires as it does the players.
"Calls can sometimes affect a game," Lester said. "They're doing the same thing we are. They're out there busting their butt to do the right thing. Sometimes they get it right and sometimes they get it wrong. That's part of the human element of baseball."
The crew chief, Joe West, was asked about the close plays by a pool reporter following the game.
"They were three bang-bang plays at first base," West said. "It seemed like two of them went against the Red Sox, one of them went against the Angels. ... From where I was, it's the kind of play, they hit the bag at the same time. I'm sure that the camera slowed everything down and they deciphered it the way they did. These are professional umpires, and they get in the best position they can to make the call. He was in great position on all the plays. If he got blocked out, he got blocked out. He was there to make the call. It didn't appear that any of them were real routine plays, either. Those were all tough plays."