AZ Alkmaar's Tijani Reijnders put the Dutch side in the lead in the first half but goals from Said Benrahma and Michail Antonio in the second half completed a comeback victory for West Ham at home on Thursday.
The Premier League side, who are aiming to reach a first European final since 1976, will head to the Netherlands for the second leg next Thursday.
"I hugely believe we've got a big resilience here," Moyes told reporters. "I think we have it through the club, I think we have it through the team and we'll need it.
"When it's a cup competition, it doesn't matter how you do it really and the job is to get it done. We've not got it done yet, far from it, we've got a big job to do next week."
Moyes said that despite the first-leg win the tie is evenly balanced.
"We've got a slight narrow lead but nothing more than that," Moyes added.
West Ham, 15th in the Premier League, play at Brentford on Sunday.
