The Uruguayan made history in the Reds' 5-1 win by becoming the first Liverpool player to net three hat-tricks against one club.
Pilkington, who is currently nursing an injury, wrote on Twitter: "I wish Suarez would just leave us alone!! Big bully. People moaning about defending just wait till u see the goals he has scored!
"What are you supposed to do when someone is doing that! He's been unplayable tonight!"
The Canaries currently sit 16th in the Premier League table.