DETROIT -- As the Rangers tried to sort this one out in a stunned and somber clubhouse, second baseman Ian Kinsler came to a succinct and painful conclusion.

"That wasn't good," Kinsler said. "Those are games we have to win if we're going to be a playoff team. That's the bottom line."

The Rangers didn't win despite a brilliant performance from starter Kevin Millwood and despite having a four-run lead with six outs to go. Instead, the Tigers scored six runs off relievers C.J. Wilson and Warner Madrigal in the bottom of the eighth inning and finished off a sweep with a 6-4 victory over the Rangers at Comerica Park on Sunday afternoon.

Millwood allowed just four singles over seven scoreless innings but had nothing to show for it after the Rangers' 4-0 lead disintegrated in the eighth that included a crucial error by rookie shortstop Elvis Andrus.

"I don't think you can ask Millwood to do any more than he did today," manager Ron Washington said. "He was masterful. We needed to get those last six outs, and we didn't get them. We had the right people in there, and we didn't get it done."

The Rangers, who swept the Indians to open the season, have lost eight straight at Comerica Park going back to 2007, including three this weekend. They'll be back here May 19-21.

"The most frustrating is we started out with a sweep and then came in here and got swept," Millwood said. "We're a better team than that, that's the frustrating part."

The Rangers may be a better team, but their bullpen has set off some alarm bells during the first week, especially after Sunday. Rangers relievers have a 9.19 ERA after six games, having allowed 16 earned runs on 20 hits and 11 walks in 15 2/3 innings.

"Results are judge and jury," Wilson said. "This is a results-based game. This is the big leagues. Milly pitched great. It's a shame to let the team down like that."

Washington made it clear that Wilson is still one of his main setup relievers.

"We trust C.J.," Washington said. "I thought Madrigal did a good job ... made some good pitches. We're going to keep giving them the ball and know they'll get better. I don't want them to hang their heads."

Millwood was staked to a lead right away when Josh Hamilton hit a two-run home run in the first and Kinsler did the same in the third to make it 4-0 against Tigers starter Edwin Jackson. But the Rangers managed just two hits the rest of the way, and Hamilton, despite the home run, wasn't happy when he grounded out to short with runners at second and third and one out in the fifth.

"I have to do a better job there," Hamilton said.

The Rangers did not have a runner on base the rest of the way. Tigers pitchers retired the last 14 batters they faced. Over the three-game series, Rangers hitters were 1-for-28 against relievers.

The Rangers could have used that kind of relief on Sunday. They didn't get it. Instead, the trouble started when Wilson fell behind Inge with two straight balls, then tried to throw a fastball for a strike. Inge hit it into the right-field seats for a leadoff home run.

Wilson got ahead, 1-2, on Adam Everett, but the Tigers' No. 9 hitter was able to dump a changeup into right field for a single. Curtis Granderson then followed with a broken-bat, soft liner toward Andrus at short.

Andrus charged it, trying to catch it on the fly, and the ball skidded through just between his glove and the ground for an error.

"That's a tough play," Kinsler said. "You have to commit one way or the other, commit to catching it in the air or on the bounce. He committed to catching it in the air and didn't get there."

Placido Polanco, who had two of the four hits off Millwood, followed with a sharp, high chopper over third baseman Michael Young's head for a double, scoring one run and leaving runners on second and third.

Wilson struck out Magglio Ordonez for the first out, then walked Miguel Cabrera intentionally to set up a double play. The Rangers aligned their infield that way, including Young at third. But Carlos Guillen ripped a grounder down the third-base line between Young and the bag for a two-run double to tie the game.

Washington brought in Madrigal, who intentionally walked Marcus Thames to load the bases and then struck out Gerald Laird. But Inge, chasing a fastball outside the strike zone, singled up the middle to give the Tigers a 6-4 lead.

"Fastball, way outside," Madrigal said, shaking his head in disbelief.

"Obviously, sometimes the breaks go your way, and sometimes they don't," Wilson said. "I broke a couple of bats, and they didn't go for outs. I couldn't stop the bleeding. That's pretty much it."

Millwood didn't blame him.

"Today we had one bad inning, and it was enough to lose a ballgame," Millwood said. "Anytime C.J. comes in behind me, I feel good about it. I feel he can get the job done. It was just a bad day."