"We couldn't get that two-out hit in the last couple of innings," Millar said.
First baseman Lyle Overbay, who saw a 15-game hitting streak end Thursday, made two of the six outs, grounding out to third in the seventh and making the final out of the game against Rangers interim closer C.J. Wilson.
Millar flew out to left with runners at second and third to end the seventh. Aaron Hill and Alex Rios made outs with Marco Scutaro at second in the eighth. And Scott Rolen struck out against Wilson preceding Overbay's groundout to end the game.
"Normally, we wind up with a couple of runs," Jays manager Cito Gaston said. "Tonight we couldn't."
The inability to come through wasted a strong effort from Romero, who was 1-2 with a 7.17 ERA in three starts since returning from the Minors, where he rehabbed an oblique strain.
The big concern was the seven home runs the former sixth overall pick of the 2005 First-Year Player Draft had allowed in 16 1/3 innings since coming off the disabled list.
Romero used his changeup and two-seam fastball to keep the ball in the park Thursday. It helped that it had rained steadily starting Wednesday night, leading to a rainout and making the air a little thick at Rangers Ballpark in Arlington.
Still, the Rangers never threatened to take Romero deep.
"We made some progress," Romero said. "I've got my changeup back. And my two-seamer was pretty good, too. I threw too many pitches."
Romero did need 99 pitches to get through 6 1/3 innings, but still he was difficult to hit from the start for a high-scoring Rangers offense that only scored four runs in the three games.
Romero had seven strikeouts, including two on All-Star second baseman Ian Kinsler. One of those strikeouts of Kinsler came in the fifth inning, when Romero had trouble with the bottom of the Rangers' order, putting two men on. He bounced back to fan Kinsler and induced a groundout from Michael Young.
"He was tough right away," Rangers left fielder David Murphy said. "He had a good fastball and he was painting the corners. We knew it was going to be a tough game."
The Rangers scored their only run in the bottom of the second. Nelson Cruz led off with a single on a 1-0 pitch. Romero got to 2-2 against Murphy in the key at-bat of the game, but he hung a slider and Murphy crushed it for a double. Cruz advanced to third on the double, and Marlon Byrd plated the only run with a sacrifice fly to left.
"I was looking to bounce a slider [to Murphy]," Romero said. "I left it up a little bit and it stayed high enough in the zone."
The Jays did come away from Thursday with a more confident Romero. With two wins in Texas, they are still right in the thick of the American League East race, three games behind Boston, which finished off a three-game sweep of the New York Yankees on Wednesday.
"Winning two out of three is good," Millar said. "We're right there. We just need to keep winning games."