New Manchester City striker Wilfried Bony scored twice as the Elephants won 3-1 to earn a tie against DR Congo.
"I think we have beaten the best team in the tournament," said Renard.
"We needed to be very well-organised and try to counter a team who are very strong individually,"
Renard led Zambia to the Africa Cup of Nations title in 2012 and added: "When I was with Zambia, the Ivory Coast were better than us but we won on penalties in the 2012 final.
"You need to be realistic in football and put in place the tactics to win a game."
Speaking about the win over Algeria, he added: "In terms of football and ball control they were better but we countered with players like Max Gradel, Gervinho and Wilfried Bony.
"In football you can't afford to think you're better than you are. You need to choose tactics to fit the players you have."
Algeria coach Christian Gourcuff agreed with Renard's comments and as a result had no complaints about his side's performance.
"It was not the best team that won. I can't reproach the players for anything. We had a good few chances that we didn't take," he said.
"The El Arbi Hillel Soudani chance in particular was a great one, and the goal we lost at the set-piece was cruel."
Algeria had to face Ivory Coast after finishing runners-up in Group C to Ghana.
"I think the regret we can have is the goal we lost at the end against Ghana, which led to us playing the Ivory Coast.
"But the way we dominated against the Ivorians gives us plenty of hope. If we played the same game 10 times we wouldn't lose it 10 times."
Ivory Coast coach Herve Renard said the tournament's best team are out after his Ivory Coast side beat Algeria to reach the Africa Cup of Nations semi-finals.