Jack Jebbs struck twice and Chuba Akpom also scored in the 3-1 win.
Laraman told arsenal.com: "I'm very proud of the boys. We've had a couple of tough ties but I don't think they come much tougher than that. Everton are a top academy, they teach their boys to play the right way and it was a very difficult game. We went in at half-time 2-0 up and we wanted to stay on the front foot. But we didn't do that in the second half and they score within two minutes. It was a very difficult quarter of an hour but we rode it out and played some good stuff towards the end.
"We created a few more opportunities and then Jack Jebb bent in a free-kick. I was just pleased that they put on a performance that suits the Club and its philosophy. Of course there are improvements we can make but we went about our business in the right way."
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