A dramatic 4-3 win at Swansea City on Saturday stretched the Carrow Road club's unbeaten run in the Premier League to nine games and 10 matches in all competitions.
There was a fear Norwich could suffer from second season syndrome having admirably finished in 12th place under former boss Paul Lambert on their return to the Premier League in the last campaign.
But the victory over Swansea moved them nine points clear of the relegation zone and they are also looking ahead to Tuesday's Capital One Cup quarter-final against Lambert's Aston Villa.
Pilkington, a £2million signing from Huddersfield Town in 2011, said in The Sun: "We look like beating anyone at the moment.
"There were a couple of games where we didn't do ourselves justice but we have picked up and are scoring goals which is a bonus.
"We always believed in ourselves and knew we could pick up points in this league as we did last season. We have proven that we are more than good enough to be here.
"We've been solid at the back for a while and have kept a few clean sheets. That is one of the reasons why we are unbeaten in nine.
"We are doing well in the league so why can't we have a good cup run?"