The League Two Silkmen won the penalty shootout 4-2 after the game ended 2-2 during normal time.
Campbell's men rode their luck and had to survive an onslaught from the Seasider, who were dominant through producing 27 attempts on goal to Macclesfield's five.
Yet Simon Grayson's men were reliant on a last-minute penalty from Armand Gnanduillet to send the game to spot kicks.
Macclesfield had earlier taken the lead thanks to an own goal and a Virgil Gomis effort after Ollie Turton had opened the scoring for Pool in the first half.
"It's pleasing to see how far the team has come in such a short space of time," Campbell said.
"The players played really, really well and they put in a real shift in.
"It's hard coming to a place like this and we have to respect some of the players they have, because they are top, top players.
"Yes they had a lot of play, we knew that was going to happen, but we had to deal with that and we did with some great defending and some great blocks.
"We dug in, we played some good football and yes, we got some luck with our first goal but if you don't put it in the box nothing is going to happen.
"But I thought we played really well and enjoyed some good spells.
"It was a shame we couldn't see it out in full time and we had to go through the lottery of penalties, but we'll learn from that scenario.
"But we showed great character to come through those penalties and Owen Evans makes a great couple of saves and then scores the winning spot kick, so hats off to him.
"I'm so proud to see how the lads are growing and how hungry they are to go to the next level."