Rice's Jordan Stephens threw a complete game shut-out, sending a career-best 11 batters down on strikes.
"We had way too many strikeouts today," said left fielder Tyler Baumgartner. "Part of what we want to do is be more aggressive, that's what we've been working on the past couple of weeks. We didn't do a good job of it tonight or last night."
Stephens took a perfect game into the fifth inning before Baumgartner hit a one-out single. Baumgartner was caught stealing.
Tommy Thorpe allowed a Ford Stainback game-opening lead-off single to score before shutting the Owls out over the next six innings, but took the loss.
"Tommy I think did a fine job," Horton said. "He probably made a mistake on the lead-off, left a ball over the plate. They did a good job of getting inside of him. Their 3-hole hitter hit a pretty quality pitch and that was the story of the game."
Thorpe was the beneficiary of excellent defensive support, including a Baumgartner throw that beat Christian Stringer at home in the third to save a run.
"That was a great play by Tyler. I'm glad he threw him out. I was excited. You couldn't ask for any more," Thorpe said.
Oregon only placed runners in scoring position twice. The first came when Connor Hofmann led the sixth off with a hit by pitch and stole second, but Stephens struck out the next three batters. Ryon Healy reached on a lead-off bunt single the next inning and advanced to second on a sac bunt, but once again was not advanced.
Horton was defensive of his batters, choosing to praise Stephens effort, rather than criticize his own.
"I'm not going to blame our offense. I'm not going to blame the hitters that are going up there. It might look easy to hit from the dugout or the stands but that guys is awfully good.
"We're not the greatest hitting team and we're dinged up. We've got some guys out there giving us everything that we have. Just getting a lot of hits isn't the strength of our team and hasn't been all season," Horton said.
Oregon will have to win three games in order to advance to the super regional, one over San Francisco and two versus Rice.
"Just knowing my team the way I know it… we're not going to use any excuses," Horton said. "Right now it's about survival. I'm personally looking forward to seeing my group of warriors get after that challenge."
The Ducks will play the San Francisco Dons Sunday at noon. If Oregon wins, the Duck would play Rice at 4 p.m. Cole Irvin will pitch for the Ducks.