The Buccaneers headed into the clash at the 30 June Stadium in Cairo needing only a draw to book their place in the final after a goalless first leg in Johannesburg. Twice they took the lead through goals from Relebohile Mofokeng and Mohau Nkota, but the Egyptian side fought back each time and eventually clinched the tie.
Speaking after the match, Riveiro congratulated Pyramids on their progress but made it clear he was proud of his team's efforts.
"Congrats to Pyramids for reaching the final. Also, congratulations to our players for the fantastic performance they gave and to all of our fans," said Riveiro at the post-match press conference.
"This season has been second to none. We are out of the competition today after losing our first match in the whole tournament."
The Spaniard admitted the defeat was "tough to swallow," especially given how well Pirates performed away from home against strong opposition.
"We'll need a little bit of time because I think it's a very cruel result. I think we played a really good game, a top performance away from home against an excellent team."
Pirates' exit denied South African football a historic all-PSL CAF Champions League final after Mamelodi Sundowns secured their place in the tournament's climax.