A lacklustre game ended in stalemate after Scotland international McGregor made two brilliant saves from Peter Crouch, while Stephen Ireland had a goal disallowed and Ryan Shawcross hit the crossbar.
Hull manager Steve Bruce was excused post-match media duties due to a sickness bug, and it was left to skipper Davies to pay tribute to McGregor's heroics.
He told Sky Sports: "It was a boring game, a 0-0 on a bobbly, windy pitch, but it's another point towards survival.
"I thought we were lucky to get a point in the end. Allan McGregor saved us, he made a couple of great saves.
"We were making mistakes in the second half and they were capitalising and creating chances. Neither team looked like creating chances without mistakes."
Ireland's effort, which was immediately ruled out, came following up after McGregor saved a head from Crouch, who for once had got away from Davies.
"Every time the ball gets in the box you've got to look out for him," said the defender.
"There was once I let him get away because I was worried about the second run from Stevie Ireland and he almost scored."