"It's early in the season, and I like our lineup against lefties," Teixeira said. "You look at that lineup tonight; that's a lineup that's going to score runs. It didn't happen tonight, but we'll score runs."
It hasn't helped that designated hitter Alex Rodriguez is off to a slow start, going hitless in four at-bats Wednesday with two strikeouts as his average dropped to .136. Yankees manager Joe Girardi said that he is not worried about Rodriguez at the plate.
"I think he's looked OK. I think he's looked fine," Girardi said. "Older guys can take a little while to get going in Spring Training; that doesn't really concern me. I thought he just missed a couple balls tonight, I thought he swung the bat pretty well in Detroit."
Hicks was elevated to the No. 2 spot, as he was on Opening Day against Astros lefty Dallas Keuchel, but was held hitless. Girardi said that he was encouraged by some of the hard outs that his lineup produced.
"I thought we had some pretty good swings and some guys just missed some balls, so I don't think this will be a pattern," Girardi said.
Chase Headley said that the addition of Hicks and Starlin Castro, who went 0-for-3 with a walk as the No. 6 hitter on Wednesday, have made the lineup seem less vulnerable.
"Especially when Tex went down [last season], it felt like it really was exploited then," Headley said. "Obviously with Hicks and Castro in the lineup, you've got Tex back there, I think we're just fine facing those guys."
Teixeira said that it will be vital that he and Rodriguez both begin to hit home runs against left-handed pitching; just six of Teixeira's 31 homers last season came off a lefty.
"I'd obviously like to, because in today's game, you don't get 15 hits a night," Teixeira said. "You don't score five and six runs on a bunch of singles. The pitchers are just too good, so you have to hit home runs. Hopefully that'll happen this year right-handed."
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch, on Facebook and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.