"He added: "We just keep getting on with it, that's my focus and my team's focus". "When you are us, you can't go out every week and play fantastic, you have to fight for it".
Garlick also insisted the club were not now looking for a replacement for Dyche, despite rumours over his future.
But the Everton hierarchy look set to broaden their search for a new manager with Dyche firmly in their sights. "There's one person on our list and that's Sean Dyche".
During his tenure, Dyche has guided Burnley to the Premier League twice and kept them in the division last season with a record that saw them collect 33 points at home.More news: Kevin Spacey is being 'evaluated' following sexual assault allegations
Everton have lost both of their games under current caretaker manager David Unsworth so far, losing 2-1 to Chelsea in the Carabao Cup fourth round and being beaten 2-0 by Leicester in the Premier League on Sunday, leaving them 18th in the table.
"Who knows? I'd have to consider that, if that phone call happens", Allardyce told beIN SPORTS.
Whatever the truth is, Dyche is an underwhelming choice as Everton boss.
"Is fifth like the new 25th or something?" he said jokingly after the game.