Love, appearing on ESPN Radio's "Mike & Mike" on Wednesday morning, responded to comments made by Taylor, who said Tuesday that the All-Star forward may get exposed for his play on the defensive end and may wind up being the scapegoat if the new-look Cavs struggle.
"I think emotions are definitely running high right now," Love told "Mike & Mike." "For Glen to say that, I just think that he should be focusing on the players that he just received. I mean, he has two of the No. 1 picks in the last two drafts: Andrew Wiggins and Anthony Bennett. He has another guy who can really play in Thaddeus Young.
"I think he got a lot for me. So I'd be focusing even more on that. More than anything, I'm just excited to start my time in Cleveland, get to work with my new teammates, and start with this new family here."
Love said Tuesday that he felt he had a good relationship with Taylor during his six seasons with the Timberwolves.
Taylor, meanwhile, took to the radio to offer his thoughts on how Love will fare in Cleveland.
"I think where maybe he got away with some stuff not playing defense on our team, I'm not sure that's how it's going to work in Cleveland," Taylor said on ESPN Radio 1500 AM in the Twin Cities on Tuesday. "I would guess they're going to ask him to play more defense, and he's foul-prone.
"I question Kevin if this is going to be the best deal for him, because I think he's going to be the third player on the team," Taylor added. "I don't think he's going to get a lot of credit if they do really well. I think he'll get blame if they don't do well. He's around a couple guys that are awful good."
Taylor also questioned the durability of Love, who has twice suffered a broken hand, which caused him to miss most of the 2012-13 season.
"The only thing I still have a question mark about is health," Taylor said. "I had that concern then [when they negotiated his previous contract], and I still have that concern. I think Cleveland should have that concern, too."
Dallas Mavericks owner Mark Cuban said he understands how any owner can make the mistake of making disparaging remarks about an outgoing player.
"We're competitive too. I would compare my competitive nature to any athlete in the world," Cuban told ESPN Radio's "The Herd" on Wednesday. "Business is a sport where you can be 24 by 7 by 365.
"... You try to hold back some time and take the high road. Sometimes you do. And sometimes it slips."
Brian Windhorst of ESPN.com contributed to this report.