The Toffees are at home to Oldham Athletic in an FA Cup replay tonight, with the winner earning a quarter-final tie with Wigan Athletic.
Moyes, who must also prepare his side for a Premier League clash with Reading on Saturday, concedes that his team need the boost of a prolonged cup run to help maintain their push for Champions League qualification.
He told The Sun: "We are in a period of big games and these two weeks are huge for us.
"I think we will see which way our season is going after that. A Cup run keeps you on a roll, and our bad run has been more about the fact we have not finished teams off recently."