Davies grateful for stroke of fortune
The central defender opened the scoring in the 14th minute when Jake Forster-Caskey failed to clear a looping header off the line.
Hull added a second before the break as a Robert Koren free-kick found the net via a slight deflection and were able to set up a last-eight clash with Sunderland at the KC Stadium despite Leonardo Ulloa's second-half reply for Brighton.
Davies was pleased with the spirit his side showed and now has his sights set on a semi-final tie at Wembley.
"To get the two goals, no matter how flukey the first one was - it was good to take that into half time," he told ITV Sport .
"We knew in the second half we had to give it a good go, (but) we started sloppily and once they got the goal it was a nervy last 20 minutes.
"But we've done enough - that's the main thing - to get to the next round, and now (we're) into a quarter-final with a home tie and a good chance of going into the semi-finals at Wembley."
Hull boss Steve Bruce will come up against one of his former clubs when League Cup finalists Sunderland visit, adding a touch of extra spice as far as Davies is concerned.
"It does (matter), particularly against Sunderland because of the gaffer. It's a big game," he added. "Sunderland are already in a cup final and will be trying to do well in both.
"It'll be an interesting game; hopefully we can come out on top."
Brighton defender Stephen Ward admitted their slow start to the tie proved costly, but took heart from his side's second-half revival.
"We gave ourselves a bit of a mountain to climb," Ward told BBC Sussex. "But credit to them (Hull), they started really well and are a really good side.
"I thought (in the) second half we were outstanding, (and) unlucky not to force extra-time.
"We did ourselves proud on the night, especially in the second half."