But Matt Phillips fired home from 25 yards on 61 minutes, though, and then crossed for Charlie Austin who headed home 12 minutes later.
The result leaves Blackpool outside the play-off places.
"It's a cliche but it was a game of two halves," said Thompson. "We maybe lacked a bit of quality in attack in the first half but we still created three or four good goalscoring opportunities.
"We spoke to them at half-time and said it's the decision making in the final third that wins you games and we just didn't seem to have that in the first half, that little bit of quality.
"We were punished for that in the second half. We know how good they are and how good their squad is but Harry Redknapp has just told us we should have been 2-0 up in the first half.
"The goals were a combination of errors. The deflection for the first goal after we gave the ball away and perhaps the second was just a quality goal - a one-two and a cross and a good header.
"Matt [Phillips] had a say in two pivotal moments in the game."