Before Wednesday night's game, West called the AL East rivals "embarrassing" and "a disgrace to baseball" for slowing the pace of their games to a crawl, according to the Bergen (N.J.) Record.
The teams' season opener on Sunday took 3:46 to play. Tuesday night's game went 3:48, while Wednesday night's contest, which went 10 innings, was finished in a relatively brisk 3:21.
"They're the two clubs that don't try to pick up the pace," said West, the chief of the umpiring crew working the three-game series, according to the report. "They're two of the best teams in baseball. Why are they playing the slowest?
"It's pathetic and embarrassing. They take too long to play," he said, according to the report.
During Tuesday night's game, home plate umpire Angel Hernandez denied a number of requested timeouts in the batter's box.
West did not allow Hernandez to comment, according to the report.
"All of baseball looks to these two clubs to pick up the pace," West said, according to the report. "[Hernandez] did everything he could. The players aren't working with us."
Yankees closer Mariano Rivera, asked Thursday by the New York Post about West's comments, said: "It's incredible. If he has places to go, let him do something else. What does he want us to do, swing at balls?"
When reached Thursday by ESPNBoston.com for the Red Sox's response to West's comments, general manager Theo Epstein's response was brief:
The occasionally slow pace of the game has gotten baseball's attention before. After Game 4 of last year's World Series, in which Yankees catcher Jorge Posada walked to the mound to visit CC Sabathia eight times in a single inning, MLB vice president of umpiring Mike Port said frequent mound meetings by all teams would likely be discussed during the offseason.
During spring training, Red Sox closer Jonathan Papelbon told WEEI.com: "Have you ever gone to watch a movie and thought, 'Man, this movie is so good I wish it would have never ended.' That's like a Red Sox-Yankees game. Why would you want it to end?"
He added: "If you don't want to be there, don't be there. Go home. Why are you complaining. I'm not going to sit somewhere I don't want to be. If you go to a movie or any entertainment event and you like it, you're going to stay and watch and you're not going to want it to end. If you don't, then you won't. Why is it such a big deal?"
Baseball has tried speed-up rules and guidelines in recent years, with varying results. Papelbon was fined a few times last season for taking too long to pitch, and on one occasion had a ball called on him for that reason. And hitters have been encouraged to stay in the batter's box.
One trip to the mound is allowed per inning -- by a manager or coach -- before a pitcher must be pulled. There is no limit, however, on players-only meetings.
Information from The Associated Press was used in this report.