The Ghana Premier League champions needed two second-half goals from Elvis Opoku and Derrick Sassraku to progress to the next round on a 2-1 aggregate.
"I can't actually describe the feeling after the game. In fact, I'm the happiest man around now because our hard work paid off," Abubakar told Goal.
"The first-half was a bit uninspiring but the players adhered to my instructions after the break and we had two important goals to make it to the next stage. I'm happy and will thank the supporters because they were massive," he added.
Aduana will now meet Algerian side ES Setif in the last qualifying round with the winner making it to the group stage and, Abubakar believes they can make it for the first time.
"This is the first time we've progressed to the next stage in this tournament so obviously, we can make another progress. We are with high hopes that we will make it to the group stages so we won't over celebrate this victory," he said.
Aduana will host Setif in the first leg during the weekend of March 8-10 before travelling to Algeria for the return fixture a fortnight later.