"I'm definitely excited but you can't get too ahead of yourself. We've still got around 20 games to go," 25-year-old Barnett told BBC Radio Norfolk.
"From everybody who is not playing to John Ruddy in goal, if we all chip in I can't see why it won't pay off."
Saturday's 2-1 win at strugglers Sheffield United extended City's unbeaten run to six league matches and leaves them five points adrift of leaders QPR.
Barnett has been a regular in Paul Lambert's side since joining from West Brom on loan in August.
And after being impressed by the quality at Carrow Road he turned the switch into a permanent move in January.
"I came here and I wanted to play and I knew as soon as I came in the boys play football here," he said.
"And if they play football I knew that they would be there or thereabouts at the end of the season, I'm fortunate to have these players around me."
Meanwhile midfielder Andrew Crofts was delighted with his double strike at Bramall Lane, taking his tally to six for the season.
"I've always said goals are a bonus but I like to think I give other things to the team," he said.
"But six isn't bad and I'll keep building on that hopefully.
"I'm one that every game I play in I want to give it my best.
"It was a tough battle out there, we'll always be in the game and it's a never say die attitude from the boys."
Source: BBC Sport
Source: BBC Sport