The visitors led inside six minutes through Nick Powell and Michael O'Neill's team should have had more in a first half full of chances.
But Preston did salvage a point thanks to a brilliant curling effort from midfielder Ben Whiteman.
McAvoy said: "It was a good point. I felt Stoke in the first half caused us lots of issues if I'm brutally honest. I felt they were the dominant team.
"I thought we started well in the second half but I think they are probably the best team we have played.
"They've probably caused us the most issues of any team we've played in this league."
However, McAvoy noted his side coped better after a mid-game tactical switch.
He added: "I felt they were the better team in the first half. But once we changed it (tactically) you could see us growing into it.
"We dropped Sean Maguire back and DJ [Daniel Johnson] and went with two number 10s ourselves.
"We were getting the wing-backs a bit higher up the pitch and I was delighted with Ben's strike to make it 1-1 but Daniel [Iversen] had made a fantastic save just before it to keep us in the game."
Stoke were particularly threatening with pace down both flanks, the lively Josh Tymon once again impressing for the Potters.
Preston had goalkeeper Iversen largely to thank for the point after the on-loan Dane made a string of excellent saves.
O'Neill agreed his team should have left Deepdale with all three points.
He said: "I thought for the first 45 minutes we were terrific. There were two or three chances where we should have done better and then we concede the free-kick.
"It's a great free-kick with pace and it's gone over the top of the wall.
"I thought in the second half we were terrific as well, the dominant team really. We created chances and we just couldn't find the goal.
"We're disappointed we didn't come away with three points but it's a very good performance and we'll have to settle for the point.
"There's a lot of games in the division like this. You can easily come away and lose a goal in the last minute but importantly we kept the consistency in our play.
"We were brave, we've come away from home and to develop the ball in the way we did, and to play the way we did, was testament to the work we have done with the players."