The Cavs have won just one of their last five games, leaving them fourth in the Central Division.
Grant told ESPN: "The lack of effort is just not acceptable. It's not who we are and who we want to be. It's got to be addressed head on. There's no excuse for that, but we've seen our guys compete and execute consistently and that's really what we've got to do a better job of.
"We're all accountable for it, including myself. It's frustrating. It's disappointing to our fans. The fans deserve better. That's hard, but we've got a very experienced, creative dynamic group of people who are working on a daily basis to help us become more consistent.
"We know it's there. Our guys, they're learning, they're growing and we have expectations for them and for ourselves. It's disappointing. We feel that every day."
The Cavaliers face the New York Knicks later today.