The Pharaohs moved a step closer to their dreams on Tuesday with a 1-0 home win over second-placed Uganda.
The seven-time African champions sit top of Group E on nine points, two and five ahead of the Cranes and the Black Stars respectively while Congo sit bottom with just a mark.
"We were under a lot of pressure but we managed to achieve what we wanted," Cuper said after Tuesday's hard-fought win courtesy Mohamed Salah's sixth-minute strike.
"Whoever can’t withstand the pressure shouldn’t join us.
"I acknowledge the big role of the fans today. They supported us when we started to feel tired.
“We want to win all the remaining games. We’ll focus on Congo first and we aim to achieve victory.
"If the win don’t secure qualification [against Congo], we’ll be aiming to win against Ghana.
"We only think of winning. Our fate is in our hands."
Egypt host Congo in October on the penultimate matchday before wrapping up their campaign against Ghana away in November.
The Pharaohs are hoping to play at the World Cup for the first time since 1990.