The Orioles struggled in all phases, allowing 16 hits against just seven of their own and committing three errors.
The O's have lost six of their last eight games and now sit five in back of the Yankees in the American League East.
"I'm not going to get into that, 'Woe is me,'" Showalter said. "We haven't had many of these. We had a couple tough games here, and I know our guys will respond."
Hammel in particular hasn't had any nights like Wednesday this season.
His blistering start to 2012 had him looking like a potential starter for the AL in the All-Star Game. The right-hander entered Wednesday with an 8-2 record, and his 2.61 ERA was the sixth-best in the AL.
Those numbers took a drastic turn against the Angels, as Hammel allowed a career-high eight runs on eight hits and three walks in a season-low 3 1/3 innings. Before Wednesday, he had given up no more than four earned runs in any of his 14 starts, lasting at least five innings in every one.
Hammel's ERA ballooned to 3.29, knocking him down to No. 10 in the AL.
"There haven't been many people pitching better than Hamm, and he gets a mulligan," Showalter said. "He had pretty crisp stuff. Just one of those nights where nothing seemed to go his way."
Although half of the hits Hammel gave up were grounders, his command was off throughout the night. He threw 46 of his 76 pitches for strikes.
The hardest hit Hammel gave up was Torii Hunter's solo home run in the first inning, which snapped his streak of 19 consecutive innings without allowing an earned run.
"I didn't set the tone very well and I wasn't able to pitch inside," Hammel said, citing poor fastball command as his biggest issue. "[They're a] good-hitting ballculb, not necessarily power, but just putting it in play. They're going to put the bat on the ball and put it in play somewhere, and that's what happened tonight."
The Angels wore him out with knock after knock in the third and fourth.
Hammel quickly got two outs in the third before Mike Trout singled on a grounder to right. After Hunter and Albert Pujols worked back-to-back walks, Kendrys Morales grounded a single up the middle to extend the Angels' lead to 3-1.
The Angels went back on the attack in the fourth, as Alberto Callaspo hit a leadoff double to right, and Howie Kendrick scored him with a single. Trout later scored Erick Aybar on a swinging bunt single that traveled about five feet.
Hunter was next, and he flared a soft line drive past the outstretched glove of Brian Roberts, scoring Bobby Wilson and ending Hammel's night.
"It was more or less just me getting behind, or trying to do too much," Hammel said. "They were sitting on the sinker down, that was the one pitch that I was throwing down in the zone, getting behind with that. Then you've got to come to them over the plate, and they put the bat on the ball."
Activated from the 15-day disabled list just hours before the game, Matt Lindstrom entered from the bullpen and also struggled.
Trout scored when Matt Wieters' throw to third base went by the glove of Wilson Betemit, and another grounder off the bat of Morales scored Hunter. Two batters later, Callaspo hit his second line drive to right in the inning, this one scoring Pujols to cap the six-run frame and make it 9-1.
Two days into a stretch of 13 games in 13 days, the Orioles had to use five bullpen arms on Wednesday.
Kevin Gregg allowed two runs in the fifth, before Darren O'Day allowed two more in the seventh.
"Obviously, it taxed the bullpen, too," Hammel said. "Overall, just a [bad] night."
Despite early signs of life, the Orioles' offense didn't fare much better.
In the first inning, J.J. Hardy nearly provided a spark, slamming a fly ball to right-center field that Trout caught when he fully extended his left arm to make a leaping grab and rob Hardy of a homer.
Chris Davis then broke an 0-for-29 slide with a single and scored when Adam Jones grounded a double into the left-field corner.
But Angels starter Jered Weaver and two relievers combined to hold the O's scoreless after that, with only five hits and a walk in the final eight innings.
The Orioles have scored only 14 runs in their last nine games, and haven't scored more than three since June 16.
The O's went 0-for-6 with runners in scoring position, and are 2 for their last 47 in those situations.
"It's always frustrating," Hardy said. "Whenever we get runners in scoring position, we always want to get them in. [It] just hasn't been going our way lately."
The only plus Hammel could find on a night he'd like to forget was that the knee soreness he has dealt with in recent weeks was gone.
"It's going to sit with me for about 24 hours," Hammel said. "I'll get some sleep, but obviously I'm not too happy about it."