The Elephants can look forward to a last-eight showdown with Algeria after Max-Alain Gradel's first-half strike secured a 1-0 win against the Indomitable Lions and clinched first place in Group D.
"For a team like this the Africa Cup of Nations begins in the quarter-finals because to go out before is a failure," said the Frenchman.
"If you don't get through with a team like Cameroon or the Ivory Coast or Senegal you get the finger pointed at you.
The Elephants have improved after a sluggish start that saw them play out 1-1 draws with both Guinea and Mali, and Renard added: "I said before this game that it's not necessary in a Cup of Nations to start too quickly because it's a very difficult competition and with players like this they are ready to compete and they love games like this.
"When you play Cameroon you don't have to try to find motivation especially when we lost 4-1 to them in September (in qualifying)."
Lions leave it all on the field
Cameroon coach Volker Finke, on the other hand, insisted his team had given everything despite their 1-0 defeat to Côte d'Ivoire, which saw them eliminated from the Africa Cup of Nations at the group stage.
"I think really the Ivory Coast took advantage of a little mistake we made in the first half to score the goal," said Finke.
"We tried really hard. Everyone gave their best, so that's why we can't say the team didn't try to the end.
"In the second half everyone gave a lot but there weren't many clear chances. In the first half we had two or three really good chances but didn't score and that is the reason we lost."
Captain Stephane Mbia added: "The boys gave everything on the pitch. It's disappointing because we didn't qualify but we need to be positive because the team is young and the best is still to come."