The Indians were one of eight teams on Lucroy's no-trade list.
"Certainly, if we were at the point where we were strongly considering pursuing a deal, we were pleased with the return," Stearns told reporters, according to MLB.com. "But Jonathan's a very good player, as well, and if he's on our team going forward, we'll be happy to have him."
A two-time All-Star, Lucroy is batting .300 with 13 homers and 50 RBIs this season. He has a $4 million salary this year as part of a contract that includes a $5.25 million team option for 2017.
According to multiple reports, Lucroy had asked the Indians to remove the option year in 2017 from his contract, making him a free agent this season, a request that was denied by Cleveland. According to USA Today, the Indians would not guarantee Lucroy would be their starting catcher next season.
Cleveland has responded to Lucroy's requests by telling the Brewers it was their responsibility to appease Lucroy and get him to consent to the agreed-upon trade, a source told ESPN's Buster Olney.
"I know you guys want [details], but I'm not going to [give them]," Lucroy told reporters, according to MLB.com. "Some circumstances came up that made me void it, obviously. I think when it comes out, everyone will understand why. ... I'm not going to comment on any specifics, nothing like that, as much as I'd like to. I'm respecting their process and what the Brewers are trying to do in terms of the trade. If that's going to happen or not, I don't know. As of right now, I'm still a Brewer, and I'm going to be until somebody tells me different."
Lucroy appeared as a pinch hitter and flew out to right field in the bottom of the eighth in the Brewers' 4-2 win over the Pittsburgh Pirates on Sunday. He received a standing ovation from the Miller Park crowd.
According to reports, the Brewers would have received four minor league prospects from the Indians. Included among the prospects would have been prized switch-hitting catcher Francisco Mejia, 20, and outfielder Greg Allen, 23.
Shortstop Yu-Cheng Chang, 20, also would have been headed to Milwaukee, along with another prospect.
Lucroy had told the Milwaukee Journal Sentinel this offseason that he wanted to play for a contender.
"I want to win and I don't see us winning in the foreseeable future. I want to go to a World Series. That's what all players want. Rebuilding is not a lot of fun for any veteran guy," he said.
The New York Mets and Texas Rangers were among the teams linked to Lucroy, with New York reportedly offering a three-player package that included the club's own catcher, Travis d'Arnaud, along with a top prospect and one more piece.
The Mets were no longer pursuing Lucroy as of Sunday afternoon, a source told ESPN's Jayson Stark.
The Indians have been in the market for a catcher since Yan Gomes was put on the disabled list July 18 with a shoulder injury. Gomes, who struggled most of the first half of the season, is expected to miss four to eight weeks.
With Gomes out, Chris Gimenez and Roberto Perez have been sharing catching duties, but neither has been productive. Gimenez entered Saturday's game batting .200, and Perez is in a 1-for-23 slump. He previously missed six weeks with a broken thumb.
Many Indians players declined to comment when asked about Lucroy on Sunday, but Gimenez responded, "his loss," according to MLB.com.
The Associated Press contributed to this report.