The north African nation stunned the Group H favourites by taking a 25th-minute lead via Sofiane Feghouli's penalty, and maintained it until the 70th minute before Marouane Fellaini and Dries Mertens struck.
Bougherra insisted his side's profligacy was one reason for their downfall, and also conceded the conditions in Belo Horizonte affected Vahid Halilhodzic's men.
"Our mission was difficult today against a very good Belgian team, but unlike our opponents, we did not take advantage against our attacks," Bougherra said.
"The heat also penalised a lot. Unfortunately, we had not managed to preserve our advantage to score."
"We must not let down. Instead, he will believe in our chances to recover in the next two games we have left to play," he said.
