"[I'm] just not very happy," Holland said. "I let the team down. These are the big games for us right now. We're trying to contend for the playoffs. We want to win our division. It's just very frustrating on my part."
The Rangers are now 5 1/2 games behind the American League West-leading Angels and three behind the Red Sox, who are in control of the Wild Card spot. Both Los Angeles and Boston won on Sunday.
Holland was rattled early, giving up a double to Chad Moeller in the first inning that scored Melvin Mora and Jeff Fiorentino.
Mora scored again during the fourth when Fiorentino singled to center. Brian Roberts and Nolan Reimold each drove in runs later in the inning to give the Orioles a six-run lead.
"I had good stuff," Holland said. "I just didn't make my pitches at the right times and fell behind. I wasn't getting ahead of some people, and they were getting some key hits."
Roberts had two RBIs for Baltimore.
The Orioles claimed the final two games of the series with the Rangers, making it only their second series victory since the All-Star break. It was their third shutout of the season.
"It's very frustrating," Holland said. "These guys want it, we want it and I want it. It's just one of those days where I let everybody down."
Manager Ron Washington said that Holland "threw the ball well. He was just missing on the inner half of the plate. He didn't make an adjustment to get back out over the dish or look to another location."
Holland has pitched 115 1/3 innings in 2009 after throwing 150 with three Minor League clubs last season.
"I'm not tired," he said. "I can promise you that. I'm not tired at all. That's not an excuse at all. I just fell behind."
Said Washington: "Everybody's fatigued down the stretch, but you get over that. I didn't think being fatigued had anything to do with him being out there throwing today. It was the Baltimore Orioles not swinging at some pitches that were close."
Orioles starter Jeremy Guthrie was solid in his seven innings, striking out six while giving up six hits. He was everything the Rangers could have used on Sunday.
"To beat Texas -- you know they have a real good team -- you have to make pitches, and that's what Guthrie did," Orioles manager Dave Trembley said.
Washington watched his team's bats cool during the final two games of the series. After scoring four runs in the first inning of Saturday's loss to the Orioles, the Rangers have not scored in the 15 innings since.
Their manager's frustration was evident on Sunday.
"Of course we missed something, because we feel like we can beat them, but they are a big league team," Washington said. "On any given day, it's not the best team that wins. It's the team that plays the best. The last two days, they played better than us. A Major League team can struggle, but that doesn't mean they can't win a ballgame. I'm not taking anything from those guys. They threw up 15 innings of zeroes. What are you going to do?"
Ian Kinsler and Nelson Cruz each had two hits for the Rangers in the loss, but personal success was of little consolation for Kinsler, who said the Rangers struggled with Guthrie's offerings.
"His fastball had late life today," Kinsler said. "Basically, it was moving the closer it got to the plate. He's a guy you're going to have to battle against every time. He's a quality pitcher in the league. Today, his fastball had life on it."
Kinsler said that the team still believes in Holland despite his recent struggles.
"Anyone that we run out there, we've have a lot of faith in, a lot of trust," Kinsler said. "That's who we expect to win with."