The north African side battled past Congo 2-1 at the Cairo International Stadium to book their place in next year's showpiece, 17 years after their last appearance.
And the 25-year-old was instrumental in the encounter after scoring twice, including a 95th-minute winner.
"I can't really express how I feel, I don't quite talk so much but I'm really proud. Today we realized a long-awaited dream," Salah told Ahram.
"That was to me, a dream come true, whether as a footballer or an Egyptian citizen and fan. I'm proud I made the Egyptians happy today by scoring today twice against Congo.
"The game was a difficult one tonight and all the qualifiers were difficult games as well, today there is no big difference between every team and the other.
"When I stepped up to take the penalty, I didn't think of anything but scoring and winning the game.
"The most difficult moment in my life was when the fans fell silent following Congo's equalizer but thank God we finally realized a childhood dream of my own," he concluded.