The Buccaneers needed to win by two clear goals to overturn the deficit against Tonka Twende, who were leading 1-0 from the first leg.
Mokwena's counterpart, Aggrey Chiyangi, named a strong team with attackers Kennedy Musonda, Tapson Kaseba, and Spencer Sautu all starting.
Pirates dominated possession with Frank Mhango being the main instigator of attacking thrust for the hosts in the opening exchanges.
The Malawian attacker cut inside from the left-hand side before forcing Sebastian Mwaange into a decent save as the home side searched for an early goal against the tournament's debutants.
Bucs were looking to play early crosses into the box for Shonga, who scored five goals in last season's Champions League.
The pressure was mounting on the Eagles defence as Mhango took a shot at goal from a tight angle but Mwaange made a save with Shonga calling for the pass.
The last chance of the first half went to Shonga and the Zambian striker's effort was easily saved by Mwaange and the score was 0-0 at the interval.
The visitors' defence frustrated Pirates in the opening stages of the second half and Mokwena reacted by introducing the attack-minded duo of Kabelo Dlamini and Augustine Mulenga.
Pirates upped the tempo and Dlamini hit the upright with a thunderous left-footed shot with Mwaange rooted to the ground.
Pirates deservedly took the lead when Happy Jele scored with a powerful header from close range to make it 1-0 to the home side on the hour mark.
However, Eagles responded with a goal of their own almost immediately at the other end when Sautu played a cross to Amit Shamenda, who fired home with a low shot to make it 1-1 in the 61st minute.
Lorch was brilliantly denied by Mwaange twice before the Bafana Bafana attacker hit the upright with a powerful shot midway through the second half.
Mwaange continued to shine between the stick as he pulled off a magnificent save to deny Lorch from an indirect free-kick in the closing stages of the game.
Ultimately, the match ended in a 1-1 draw on the night with Green Eagles advancing to the first round on aggregate where they will face Angolan side Primeiro de Agosto, while Pirates were eliminated from the competition.