Jamie Vardy's late strike ensured that Nigel Pearson's side secured back-to-back wins and sent West Brom - six points above the bottom three - slumping to a third successive defeat.
"In the second half in particular, there were two or three incidents where we've given the ball away or picked the wrong pass and given Leicester the impetus," Pulis said.
"We played really well in the first half, but conceded three really disappointing goals.
"The first goal, it is lower-league stuff, a ball pumped forward and they win the first header, get on the second and score.
"But we came back well and we were the better team up until half-time."
Darren Fletcher gave Albion the lead early on, only for David Nugent to equalise soon after.
Craig Gardner's venomous volley put the hosts back in front before the interval, and although West Brom twice went close through Jonas Olsson, it was Leicester who drew level through Pulis' former Stoke player Robert Huth. Vardy then snatched the victory late on.
"You can't take anything for granted at this level," added Pulis.
"We missed a lot of chances by giving possession over – one of those was with Saido [Berahino], he had a great chance to pass to [Craig] Gardner in the box, but instead decided to shot from 25 yards – if he plays Gardner in it could've been 3-1.
"We were never out of the relegation battle, as I've said all along you need the points, and that's the main thing."
