Heaslip scored a try for his country in Dublin on Sunday as they got their campaign off to a winning start.
However, the forward believes that work still needs to be done ahead of next weekend's clash with reigning champions Wales at the Aviva Stadium.
"Huge improvements will be needed for next week," Sky Sports News quotes him as saying.
"It will be a huge challenge to go up against a team that's won this championship two years in a row."
Heaslip was handed the captain's armband against Scotland as Paul O'Connell was forced to pull out of the match before kickoff with a chest infection.