The former Juventus team-mates duelled throughout a match which remained goalless until Eder's 88th-minute winner for the Azzurri.
Ibrahimovic appeared unhappy with one Chiellini challenge on John Guidetti but insisted after the match that he holds no grudge towards the centre-back.
"Everything was okay," he told reporters. "It's all fine. If not, he'd be in the hospital right now."
"This game shows that against a team like Italy, great team that they are, you must play for the entire 90 minutes," Ibrahimovic added.
"It's not enough to play for 89. You must be cautious for the whole game."