The midfielder, on loan from Tottenham, helped provide the platform alongside fellow summer arrival Tom Huddlestone that allowed Steve Bruce's men to defy Norwich and claim the points despite losing striker Yannick Sagbo on a "disastrous" full debut to a red card with more than an hour to play.
Livermore, who turned his back on the bright lights of the capital in favour of first-team opportunities, is fully aware the Tigers will have to reproduce this fortitude on a weekly basis.
He said: "I thought it was a great team performance. Although we went down to 10 men I thought we showed great resilience and that's what we are going to need to progress in this campaign.
"I thought the lads were brilliant - composed on the ball when we had it and worked their socks off when we didn't," he told the club's website.
Sagbo had won the penalty that allowed Robbie Brady to score the only goal of the match, and Bruce said the effort shown by the players after the Ivory Coast striker's red card was evidence that the Tigers have the right fuel in the tank.
Bruce said: "To defend for an hour in the Premier League is a wonderful, wonderful achievement.
"The players have probably been moaning and groaning about the physical work they have been doing but you have to be physically up there with everyone else in the Premier League and they have shown they have been."
Sagbo was sent off for making a head-butting action towards Russell Martin, and earned himself a stiff reprimand from his manager.
"He has done something stupid on his debut and it has been a disaster for him and he will remember his debut for all the wrong reasons," added Bruce.
"Make no mistake he has been told, and severely told, but he will learn from this, that's the main thing."
The Canaries by contrast looked decidedly off colour.
After a bright start, they found themselves short of ideas about how to break down the home side, and that situation was not even helped by Sagbo's dismissal after which Hull continued to look dangerous on the break.
Apart from a powerful header from Ricky van Wolfswinkel, well saved by Allan McGregor, there was precious little for manager Chris Hughton to enthuse about.
Hughton, who described the penalty decision as "incredibly soft", said: "We didn't threaten the goal enough, and we had a really bad period in the first half where we didn't keep the ball well enough and we need to be better than that.
"We got enough crosses in but you need that one moment of real quality which was lacking from us.
"Before the game we felt we could put in a good enough performance to get something from the game so that makes it even more disappointing."