Signed on a season-long loan deal from Galatasaray last week, the Sweden international came off the bench in Saturday's 1-0 defeat at Hull but was the star performer against a spirited Bury side at Carrow Road, scoring the third and fourth goals for Norwich.
"It was perfect," he said.
"It was really nice to come on the pitch here and play, it was also nice to play 90 minutes as it is a couple of months ago since I last got 90 minutes.
"It was really fun. It is always nice to win, especially after losing at the weekend."
Despite Martin Olsson, Anthony Pilkington, Leroy Fer and Steven Whittaker all joining Elmander on the scoresheet, SkyBet League Two side Bury managed three goals of their own, although former Bolton forward Elmander always felt the hosts had control of proceedings.
He said: "We played well, we were very good.
"That is the thing with football, you can never relax no matter what team you are playing against, especially in England where everyone is fighting for the 90 minutes. But I think we had everything under control, when they scored we moved up an extra gear and scored again."
Having taken just one point from their opening two Barclays Premier League fixtures, Chris Hughton's side will be keen to pick up a first league win of the new season when they welcome Southampton to Carrow Road on Saturday.
Elmander believes the Canaries can take confidence from their performance in front of goal against Bury into the clash with Saints.
"It was nice finishing from all of the boys," he said.
"This is something we will bring to the weekend and hopefully we can score a couple of goals, maybe even six - who knows?"