A thunderbolt from debutant Omar Marmoush four minutes into the second half settled Egypt's nervous as they overtook Libya with a one-point lead on top of Group F.
Egypt laboured for much of the game despite controlling proceedings, with Libya's well-drilled defence restricting them to a few goal-scoring chances.
However, Queiroz was happy with the intense football Egypt had displayed in his first competitive match in charge.
"There is no doubt that we deserve the three points. We played good football; this was my expectation before the game," the former Real Madrid and Portugal boss told the post-match news conference.
"We just think that we should have finished the game earlier with more goals. But the players did very well with a lot of concentration. We were on top of the ball for 90 minutes. I think with the quality of our game we made them crash.
"We needed to press for 90 minutes. Our team reaction, attack and defence, was always with high tempo. That was the only way to control the Libya team."
Queiroz refused to single out Stuttgart's on-loan winger Marmoush for praise, saying he only prefers to say "it was a great goal and that the team won three points."
Egypt have seven points from three matches, one ahead of Libya and four clear of Angola. Gabon lie at the bottom with a solitary point.
Should the Pharaohs beat Libya in Benghazi in the second of a double-header on Monday, they will be in pole position to finish on top of the group and advance to the final two-legged playoff for a place in next year's World Cup finals in Qatar.
"Now that we are leading the group, We got to fight until the end to keep this position and move to the next step," Queiroz added.
"I'm sure that Libya now only think about how to get back to the first position in the group, and this is normal … It will be a very tough game, for sure, like all World Cup games."