The hosts over-ran the Tigers in the opening 45 minutes at Villa Park, netting goals via Gabby Agbonlahor and Andreas Weimann, while Fabian Delph and Ashley Westwood also both hit the woodwork.
Hull improved after the break, with Nikica Jelavic scoring with 16 minutes remaining to set up a nervy finish, but Villa held on to make it seven points out of nine going into the international break.
Lambert told Sky Sports: "I thought it was well deserved. I thought first half we should have been out of sight, I thought we should have at least scored four, and I thought the football in the first half was fantastic.
"Second half we were under pressure but I knew that was going to happen, but I thought first half set the tone for the game.
"You are never going to dominate a game for 90 minutes. You can only earn the right to play against a team and credit to Hull, they came at us strongly in the second half.
"But (Brad) Guzan never really had too much to do, even the goal has hit Aly (Cissokho) and goes in.
"And Darren (Bent) might have finished the one at the death to go 3-1 up. But I thought we deserved to win the game."
Lambert thought Agbonlahor was outstanding in the win.
"I thought he was brilliant – his running was great," said the Villa boss.
"But I just thought in general the whole team performance was excellent."