The Super Eagles defeated Tunisia 1-0 at the Al Salam Stadium on Wednesday, thanks to Odion Ighalo's first-half effort.
The victory stretched Nigeria's unbeaten record in third-place playoff matches to eight games and their winning streak against the Carthage Eagles at Afcon to five matches.
A semi-final loss to Algeria dashed their hopes of winning the coveted title on Sunday, but Iwobi sees the bronze medal as motivation for Gernot Rohr's "young" team to do more.
"It is a great achievement considering the quality of the 24 teams, especially as our team is very young," Iwobi told Caf media.
"We're happy with this medal, hopefully, we can do better in the next Africa Cup of Nations."
He picked the most difficult game he played in the tournament and also reserve praise for the fans.
"It's difficult to say, because of the quality even in the group stage against Burundi, Guinea and Madagascar," he continued.
"The toughest one was trying to overcome the team that knocked us out, Algeria. Maybe it was against them because we weren't able to win.
"Thanks to the fans for their support, we will always make them proud because of the support that they give us."