Servais said he was surprised by Clevenger's tweets and called the situation "unfortunate," but with Clevenger already on the 60-day disabled list, he didn't foresee it as a potential disruption.
"I don't believe it will be," Servais said. "We had a little team get-together last night and a few of the guys knew what had happened. A lot of guys are on social media and see what's up there. I don't anticipate it being a distraction at all.
"We've got 10 games to play and we know what's at stake and where our focus needs to be. And that's on playing a good ballgame tonight and beating the Twins. It's unfortunate. I think it surprised a lot of people. But we've got games to play."
The Mariners suspended Clevenger without pay for the remainder of the season on Friday.
"As soon as we became aware of the tweets posted by Steve yesterday, we began to examine all of our options in regard to his standing on the team," general manager Jerry Dipoto said. "Today we have informed him that he is suspended for the reminder of the season without pay."
Clevenger, who is on the 60-day disabled list recovering from a broken right hand and an elbow injury, tweeted several offensive remarks regarding the Black Lives Matter movement and the protests and unrest following the shooting of a black man by a police officer in Charlotte, N.C., on Tuesday.
Clevenger is earning $516,500 this year, so the suspension will cost him about $32,000. He is scheduled to be eligible for arbitration for the first time this offseason and is under the Mariners' control for three more seasons.
Dipoto released the following statement on Thursday after Clevenger's tweets came to light:
"The Seattle Mariners are very disappointed at the tweets posted on Steve Clevenger's account. While he is certainly free to express himself, his tweets do not in any way represent the opinions of the Seattle Mariners. We strongly disagree with the language and tone of his comments."
Clevenger issued the following apology via MLB Network's Ken Rosenthal on Friday:
"First and foremost, I would like to apologize to the Seattle Mariners, my teammates, my family and the fans of our great game for the distraction my tweets on my personal Twitter page caused when they went public earlier today. I am sickened by the idea that anyone would think of me in racist terms. My tweets were reactionary to the events I saw on the news and were worded beyond poorly at best and I can see how and why someone could read into my tweets far more deeply than how I actually feel.
"I grew up on the streets of Baltimore, a city I love to this very day. I grew up in a very culturally diverse area of America and I am very proud to come from there. I am also proud that my inner circle of friends has never been defined by race but by the content of their character. Any former teammate or anyone who has met me can attest to this and I pride myself on not being a judgemental person. I just ask that the public not judge me because of an ill-worded tweet.
"I do believe that supporting our First Amendment rights and supporting local law enforcement are not mutually exclusive. With everything going on in the world I really just want what is best for everyone regardless of who they are. I like many Americans are frustrated by a lot of things in the world and I would like to be a part of the dialogue moving forward to make this a better world for everyone.
"I once again apologize to anyone who was offended today and I just ask you not judge me off of a social media posting. Thank you and God bless everyone."
Clevenger, 30, was acquired by Dipoto in a trade for slugger Mark Trumbo last December. He played in 22 games as the Mariners' backup catcher to start the season and was hitting .221 when he broke a bone in his right hand on a foul tip on June 29.
Clevenger is a six-year Major League veteran who played in parts of three seasons with the Cubs in 2011-13 and with the Orioles from 2013-15. He went from Chicago to Baltimore in July 2013 in the deal that sent Jake Arrieta to the Cubs.
Clevenger had been rehabbing with the Mariners in Seattle the past week after his Minor League rehab stint with Double-A Jackson ended, but he did not make the trip with the team to Minnesota on Thursday.