Murray told Buffalo's WGR 550 on Thursday that Eichel told him he was the best player in the upcoming NHL Entry Draft.
Eichel attempted to clarify the comment at the combine one day later.
"I'm pretty confident in my own abilities," he said. "I know everyone's making a big deal that I said a comment like that. It wasn't me comparing myself to (projected first-overall pick) Connor (McDavid) or anything like that. It was more of me thinking that I'm the best player in the draft."
Eichel said he didn't expect Murray to go public with the remark.
"I didn't really think it was a big deal," the prospect said. "I thought that was pretty confidential within the team."
He said he doesn't see his confidence as a problem.
"I don't think it's a bad thing at all. That's why I said it. I don't know why people are making a big deal of it."
The Sabres hold the second pick and are expected to select Eichel.
The 2015 NHL Entry Draft will take place June 26 and 27 in Sunrise, Fla.