A goal from midfielder Tom Ince handed the Seasiders a vital advantage going into next week's second leg, with Blues manager Chris Hughton still confident of progression
A Tom Ince strike proved the difference at Bloomfield Road and leaves the Lancashire club 90 minutes away from a Wembley final and a chance to return to the Premier League.
Holloway expressed his delight at the manner in which his side stuck to their principles but lamented his inability to boost his forward line due to rules over substitutions.
"I'm absolutely delighted with the way that we played under pressure," he told Sky Sports.
"Everybody's under pressure in these games, and I wanted to try and play the brand of football that we do. It was going to be tough against a really good team and whatever happens it was only half time.
"Unfortunately we've only got one goal but our play merited more than that. But that's all you can ask, so we've got to go down there - it's half time, we've got a goal advantage - and see if we can impose our game on them, but it's going to be tough.
"But I'm delighted tonight, I thought we were absolutely terrific.
"I wanted to [get more goals] obviously. I've got some really decent forwards here - I didn't even pick Lua Lua on the bench.
"It makes it difficult with only five subs, I think that's a ridiculous rule. So I've had to leave a couple of really good players out as well."
Meanwhile, match-winner Ince revealed his disappointment at the Tangerines' failure to build on their advantage.
"It should have been more. In the second half we had a lot of chances, but we're happy with the one nil," he said.
"It was vital that we got something here at home, we couldn't have gone there with a draw or [if we] didn't score, so we had to go there with the advantage. It could have been more but we'll take the one."
Holloway's opposite number, Blues boss Chris Hughton, is hoping his side can improve ahead of the second leg at St Andrew's.
"We'll certainly have to improve on what we were tonight. We always knew it would be a difficult game with the way that they play," he said.
"They get a lot of possession because of the shape and the numbers that they get into the middle of the park, and all you can do is you can try to restrict them to minimal chances, which I thought we did.
"I thought they had a couple of good chances, but of course they had good possession. We didn't use the ball well enough. If I look at certainly how we've been away from home of late, whether that be in our general play or whether that be on the counter we've generally been better on the ball.
"So we need to be better than that, but we have an opportunity now to take them back to St Andrew's."
The 53-year-old also refused to blame his squad's heavy schedule - which has included a Europa League campaign - for their lacklustre performance.
"We've enjoyed the season, I haven't had any of the players telling me that they're tired and can I rest them," he continued.
"If I looked at the performance today it was down to a very good Blackpool team that will always have good possession.
"We need to threaten a little bit more. The shape that we played today tried to restrict them a little bit and play a little bit more on the counter attack. But as I said we need to be better and we've got that opportunity, which will be a full St Andrew's."