The game's solitary strike was credited as an own goal to Blues captain Curtis Davies after a wicked deflection sent Tom Ince's speculative drive beyond wrong-footed goalkeeper Colin Doyle a minute before half-time.
In the second period, Peter Ramage produced a magnificent last-ditch block to deny Seasiders forward Gary Taylor-Fletcher, before Stephen Dobbie blazed over following a sublime piece of skill from man-of-the-match Ince.
"They nearly nicked an equaliser - I'd be fuming if that was the case because, generally, I thought we deserved to just edge it," said Holloway.
"I'm delighted it (the goal) went in, I think we needed that, but a couple of those others - deary, deary me. I hope we don't rue the day that we missed them.
"Taylor-Fletcher, what a great block. That was unbelievable. That's as good as a goal sometimes."