The Lilywhites were beaten 2-0 at Goodison Park in their final pre-season friendly.
Neil's men fell behind in the ninth minute to a goal from Toffees right-back Jonjoe Kenny and looked in for a long afternoon.
However, they stayed in the game and became more competitive, seeing two good chances go begging in the first half.
Everton's second goal came in the 65th minute from Dominic Calvert-Lewin, shortly after Tom Bayliss had seen a goal disallowed for offside.
Neil: "I thought it was a tough game, Everton are a good side - when you look at their players across the pitch they have a lot of quality.
"We started poorly which was a disappointment, because they went ultra-aggressive in terms of their starting phase we really struggled to get out.
"To be honest, we should have turned it earlier to Jayden Stockley.
"Everton then got the goal and at that point I was a bit concerned because we weren't really in the game.
"We certainly didn't make it easy on ourselves in terms of the match but we had two really good chances in the first half.
"Ethan Walker got clean through and the keeper made a great save, Jayden got clean through and the keeper made a good save.
"As the first half went on we started to jump better up the pitch with Brad Potts and Tom Bayliss bumping higher up but we left that gap in behind us.
"Leading into half-time I was more pleased, the lads dug in and found a way to be effective.
"In the second half there wasn't much in it. The game changed when we scored the goal which was disallowed.
"It was neck and neck then, had it been allowed it would have been 1-1.
"Then their second goals was similar, it was neck and neck when you watch it back on the video.
"After that it became tough for us, the game got stretched because we were searching for a goal.
"Listen, we came through it unscathed. I didn't think some lads did too badly at all today, there were some good bits in it.
"In the last three games we have played three Premier League teams and lost only one of them."
North End faced an Everton side with plenty of attacking quality on show, Richarlison a particular threat - the Brazilian set up the second goal for Calvert-Lewin.
Neil said: "You had Theo Walcott who moved for whatever he did, Richarlison who is £30m worth, Calvert-Lewin who I'm pretty sure will lead the line for them all year.
"Everton are a good side, this was a good test for us and we'll have taken plenty from it."