The Baggies edged League One club Peterborough United 4-3 on penalties after it ended 1-1 at the end of extra-time at London Road.
The fourth round replay could have been settled in the final minute of extra-time if Saido Berahino had have put his pointblank header on target, something Pulis still cannot believe didn't occur, but was pleased to move through to the fifth round of the famous cup competition.
"We had the better opportunities as the game went on, we were just waiting for the net to bulge with Saido's header at the end and how he misses I don't know," he said.
"You have got to give all the credit to Peterborough. I am a traditionalist, I love this competition, it's very special to me in lots of ways. It brings back memories of being a young boy in Wales."
Albion will now head to the Madejski Stadium to take on Reading in the next round on February 20.