The signing from Chelsea featured in the 1-0 preseason friendly defeat to Roma.
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Dewsbury-Hall told evertontv: “Personally, it was an amazing feeling to make my debut here: packed-out crowd, the atmosphere, the start was amazing.
“Obviously, the result, look, it's not the most important thing today. It's about getting minutes in the legs for the lads.
“Results will come, but it was something I'll never forget, that reception at the start when they shouted my name and the lads' names.”
On the support from Everton fans already, Dewsbury-Hall added: “It's a bit overwhelming.
“I've had some really nice messages since I've got here, and that means a lot to me and my family.