"It was a crucial game. We were under a lot of pressure during the past days after the defeat against Nigeria. The players showed a great character and strong personality to win the game," Queiroz told the post-match news conference.
The Pharaohs came under fierce criticism following their tame display against Nigeria in their opening game last Tuesday, which they lost 1-0.
Liverpool forward Mohamed Salah scored a second-half volley to revive Egypt's hopes and move them up to second in Group D with three points, three behind leaders Nigeria who ensured their progress to the last 16 with two victories.
"Both teams were good on the pitch today. But without a doubt we created the most chances and deserved our victory. We had many occasions and unfortunately we had three balls that hit the post which could have changed the course of the game," Queiroz added.
Salah and lone striker Mostafa Mohamed hit the woodwork in the first half, while substitute Ahmed Zizo also had a half-volley denied by the post in the second period.
"Today we produced a good performance and the victory was important. I know we are going on the right track and the team will improve in the next games," Portuguese boss Queiroz said.
Egypt need only a draw against Sudan on Wednesday to seal progress to the knockout phase.