Andrelton Simmons' single in the fourth inning was the fourth and final hit for the Angels, whose last 14 batters were retired in order after Mike Trout's one-out walk in the eighth.
"It's tough for our guys to really go out there and pitch with our backs against the wall like they did," manager Mike Scioscia said. "We talked about this last year, until these guys really get their feet on the ground offensively and start attacking the ball like they can, these are the games that we're going to be playing; tight games and it's certainly going to put pressure on all parts of your staff, whether it's your rotation or your 'pen.
"Last year, we held up to some extent. But these guys, we need them to start swinging the bats really now."
Pujols hit his second home run of the season and the series as the Angels finished with three homers in the set after hitting three home runs in the first nine games.
Sunday's futility added to the season-long issue as the Angels have scored 36 runs -- 27th in the Majors -- in 12 games and are 23rd with a .223 team batting average.
"Yeah, I still feel good about this offense," right fielder Kole Calhoun said. "I think everybody in here feels confident. Once we get rolling and start putting some hits together as a team, and getting some big knocks when things start going our way, that's when it gets fun and things start going. When you're not getting knocks ... it's tough, but you've got to stick with it."
Calhoun is one of the few regulars producing with a .349 average, one homer and five RBIs.
Pujols' home run leaves him one shy of tying Reggie Jackson for 13th all-time in Major League history, but Pujols is hitting .196. Trout is hitting .233. First baseman C.J. Cron, who has alternated with Calhoun between the fifth and sixth spots in the order, is down to .100 this season.
"I think it's going to start with not just on one guy," Scioscia said. "There's some guys in here that just need to get into their game. Once it does, the way this lineup is stacked, I think it makes a lot sense. It's just right now ... it's tough when you've got probably four guys that really aren't swinging the bat anywhere near the way they can."
Brian Hall is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.