The hosts should have been ahead before Alan Browne scored just before the break, giving Preston a slender lead at half-time.
Pulis’ side hit back after the interval, substitute Marcus Tavernier levelling early in the second half as Boro drop down to third in the Sky Bet Championship.
“As the manager, you have to take the responsibility,” commented Pulis. “The shape we started with, we didn’t look comfortable with it.
“Whether that was the players in certain positions doing certain things for you or not, I don’t know. But once we changed it, I thought we got much more into the game and were much more productive.
“We’re pleased we got the point, but disappointed we didn’t get all three with the opportunities we had in the second half, and the three clear-cut headers in the box that we should be making the goalkeeper save.
“Having said that, I can’t be too critical of the players.
“Going to Brentford and then coming here, before the games had started, if you’d said we’d get four points, you’d bite people’s hands off because that second game is always really, really difficult.
“They’ve won their last four games at home and this is the bounce game, it’s the one that’s really difficult.”
Preston threatened as early as the second minute, but Lewis Wing blocked Brandon Barker’s shot with an excellent covering tackle.
On the quarter-hour mark The Lilywhites’ Jordan Storey teed up Tom Barkhuizen in the area but his shot clipped the post before Aden Flint cleared.
On 43 minutes a slick move culminated in Barker teeing up Browne - the midfielder firing a precise low finish into the corner.
One minute into the second half though Middlesbrough were level, Tavernier seizing onto Dael Fry’s long ball to drill home as Boro drop down to third.