Centre-half Lucketti, in his second spell at Town, began last season as captain under Stan Ternent, but the 38-year-old was told his future lay elsewhere when Clark arrived at the Galpharm Stadium in December and made only five more appearances.
Lucketti told the Examiner: "I've still got 12 months on my contract and by the time that is up I can see us being a Championship club.
"We finished the season very strongly as the manager's methods
kicked in and given the chance of a full pre-season with him, I think we'll make a big impression next time."
Lucketti added: "I'm disappointed not to have figured more under the current manager, but I like the club and I like what he has done since coming in.
"I want to fight for a place here and I intend to report for pre-season training and get as fit as I possibly can."