The series wrapped up Thursday with another disappointing day for the Sox, who lost 4-2 in front of 23,395 at Guaranteed Rate Field.
It was a deflating three games for the Sox, who were swept and trail the Guardians by seven games with 12 games remaining.
“It’s tough,” Sox right fielder Gavin Sheets said. “Obviously 162 doesn’t come down to three games. But we knew what we had to do this series and we weren’t able to do it.
“It’s frustrating, it’s disappointing, but it’s not just this series. We had to play better all season. Obviously this was a huge series and we weren’t able to pull through. They were playing great baseball. It certainly wasn’t just this series.”
The Guardians’ magic number to clinch the division is five.
“We came into this series thinking it was a very important series because we were chasing them,” Sox starter Johnny Cueto said through an interpreter. “Unfortunately it went the way it went.”
Cueto, pitching for the first time since Sept. 11 after an illness kept him from a weekend outing, allowed four runs — three earned — on eight hits with three strikeouts and a walk in six innings.
“To come up and pitch after being sick, he’s a competitor,” Sox acting manager Miguel Cairo said.
He faced a Guardians team that showcased its running, whether it was on an infield hit, going first to third on a single or legging out a triple.
José Ramírez reached on an infield hit in the first, moved to third on a single and scored on a bunt single by Andrés Giménez to give the Guardians a 1-0 lead.
The Sox tied the game with a two-out rally in the bottom of the first. José Abreu doubled and scored on an Eloy Jiménez single.
The Guardians reclaimed the lead in the third when Amed Rosario reached on an infield single, moved to third when Cueto threw wildly on a pickoff attempt and scored on a Ramírez sacrifice fly.
Steven Kwan drove in a run in the fifth with a triple and scored on another sacrifice fly from Ramírez, making it 4-1.
“They run, and they hustle, they play hard and they put the ball in play,” Cueto said of the Guardians.
The Sox got the run in the first against Guardians starter Shane Bieber but nothing else until Sheets’ eighth-inning homer. Bieber allowed two runs on seven hits with five strikeouts in 7⅔ innings.
“Bieber, he’s outstanding,” Cairo said. “He knows how to throw his fastball, his cutter, the curveball. He keeps you out off balance. And he attacks the strike zone. He makes you swing. He knows how to pitch.”
The Sheets homer cut the deficit to 4-2. Bieber exited after giving up a two-out double to Yoán Moncada in the eighth. Trevor Stephan entered to face Abreu, who represented the tying run, and struck him out.
Closer Emmanuel Clase retired the Sox in order in the ninth for his 37th save as the Guardians won for the 15th time in their last 18.
“We just fell short to a really good team,” Cairo said. “They know how to pitch, they play defense and they know how to put the barrel on the ball. You’ve got to play clean and you have to take advantage of the chances that they give you. It’s not too many.
“They’ve been playing good and it was a tough task. Our players, they fought too. Sometimes you win, sometimes you lose.”
The Guardians have a commanding hold on the division while the Sox, a preseason favorite, find themselves just two games over .500.
“Have to play for each other,” Sheets said of the team’s approach for the final 12 games. “Go out there with the same goal. Go out and try to win every game. Obviously we’ve put ourselves in a very, very tough spot. I don’t even know what the percentage is at this time, but more than anything we need to go out and play for each other.
“Play to get a win and regardless of where we’re at, we need to try to win every game.”