The Sabres fired Dan Bylsma as coach and Tim Murray as general manager on April 20 after they finished 15th in the Eastern Conference and missed the Stanley Cup Playoffs for a sixth straight season.
Eichel told the newspaper he was surprised Bylsma and Murray were fired. He earlier had denied a report made by a Buffalo radio station that said he had no desire to sign a contract extension with the Sabres if Bylsma remained coach. Bylsma was fired the next day.
"Obviously, it was a bit of a shocker," Eichel said. "I think [Sabres owners Terry and Kim Pegula] and the rest of the organization, if they think that was best for the future, then that needed to happen.
"Obviously, the last two years, Tim and Dan have been nothing but great to me. I can't say anything bad. They treated me well and took care of me. I've got to thank Tim for drafting me and Dan for being my first coach in the NHL. I learned a lot from him."
Botterill was hired May 11. Eichel said he spoke with him by phone and text prior to their meeting Wednesday.
"First impressions, he's very well put-together," Eichel said of Botterill. "He's very well-spoken. I think he's real sharp. He knows what he wants. ... Obviously, I'll get to know him more as I get to talk to him and meet him. I've heard nothing but great things from other people, peers of his that know him. I'm excited to have him and excited for the future."
The Sabres and Florida Panthers are the two NHL teams with a coaching vacancy.