Moyes was announced as Sir Alex Ferguson's successor at United earlier this month and while Baines concedes the club will feel different without the Scot in charge, he is confident the Toffees will be able to cope.
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"It will be so strange the day we walk through the door and he's not there. But football clubs live on and we'll live on, we'll move on."
Porto boss Vitor Pereira and Wigan's Roberto Martinez are the early favourites to replace Moyes and Baines believes it is up to the new manager and his team-mates to ensure the club can continue to progress.
"It was a sad day after the last game at Goodison particularly because you've been working with him for so long, he's always around, he's such a hard worker and he doesn't miss a beat," he added.
"We'll always remember what he did for the club and where he's put us, but it's up to the rest of us, the people who remain and the people who come in, to take it forward now and build on the foundations he's worked hard to put in."