The game ended in a 1-1 draw, Daniel Johnson equalising with 19 minutes left after Amaut Danjuma had given the Cherries a 37th minute lead.
North End were distinctively second best for the first 45 minutes but were much better after half-time.
Lilywhites manager Neil said: "I thought based on the second half we deserved a point.
"The first 10 minutes we started okay but then I thought our defence was too deep, Dominic Solanke was linking the game well for them.
"Our use of the ball in the first half was poor, we didn't give ourselves an opportunity to retain the ball for any length of time.
"The goal was gave away was disappointing because although in the first half Bournemouth were better than us, the goal was really cheap.
"It was a channel ball, we got under the ball and Solanke just gives Jordan Storey a bump, then the wide player gets inside Sepp van den Berg and manages to score.
"Performance wise in the first half we were disappointing.
"At half-time I said to them if you squeeze the pitch better, hold a higher line and be more aggressive, use the ball a bit better to pick that first pass out, no question there was something for us to get out of the game.
"We did all those things in the second half, our line was much higher, much more aggressive, we played a bit better although I think we can still play far better than that.
"I thought we were the better team in the second half, Bournemouth were the better team in the first half.
"They are a very good side when you see the players they have got throughout the team and the guys they were bringing on as substitutes.
"Bournemouth aren't the type of team who want to turn the ball, so you want to make sure your line is really high so that the midfield is in touch with theirs, I just felt in the first we played too deep and didn't give our midfield a chance in the first half.
"The game got too stretched and we kept giving the ball away,"
Johnson marked his recall to the starting XI with his fifth goal of the season, that his first since the 2-0 win over Coventry on December 29.
He curled a low shot into the far bottom corner of the net after intercepting a stray pass from Bournemouth skipper Steve Cook.
Neil said: "I've seen Daniel score goals like that quite a few times, I remember Birmingham away a couple of years ago when he drove up the pitch and slid it in the bottom corner with his left foot.
"That is what DJ is in the team for, if that type of opportunity opens up what DJ will generally do is slot it in rather than put his foot through in it..
"Hhe is more than capable of scoring a goal like that."
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