Two weeks ago Pilkington, a £2million summer signing from Huddersfield, missed a glorious chance to put Norwich ahead against Manchester United and then went on to hit the post in the second half before the Barclays Premier League newcomers eventually lost 2-0, but the 23-year-old was far more ruthless in front of goal on Saturday.
"What Pilkington does with his deliveries and his influence on the team is excellent," Lambert said. "To get two goals after a horrendous leg break and what happened at Old Trafford, he will be delighted."
Pilkington took just 50 seconds to put the Canaries ahead before sealing the victory with a close-range strike after making room for himself with a clever turn in the box.
Lambert's men were far superior, with Pilkington and striker Steve Morison the star performers against a Swansea team whose threat fizzled away after they pulled one back through Danny Graham following Russell Martin's strike, which put the hosts 2-0 up.
Lambert was quick to praise the mental toughness of Pilkington, who has also had to deal with the trauma of coming back from a broken leg he suffered while playing for Huddersfield last term.
He added: "I spoke to him after the United game and I just told him to continue playing the way he usually does.
"His play at Old Trafford was excellent. He just needed that goal.
"There was a little bit of pressure after what happened a fortnight ago so to come back and do it in front of your own fans the way he did was terrific."