Robert Koren's winner found the net via a slight deflection on Monday night as the Tigers booked a FA Cup quarter-final berth at home to Sunderland thanks to a 2-1 win
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.
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 Capital One 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."