The Spaniard scored his sixth and seventh goals of the competition to help the Giallorossi to a 2-1 win in Kiev - and a comfortable 5-1 win on aggregate.
Mayoral's deadlock breaker shortly after half-time effectively ended the tie as a contest.
“It was a tough game for us,” Mayoral said. “They are a good footballing side.
"We suffered at times, but we won tonight and we are through to the next round. Those are the most important things.
“I am pleased with my goals tonight, I’m pleased to have started and to have helped the team.”
After the weekend defeat in Serie A, the performance and result was much needed going into Sunday's huge meeting with Napoli.
Mayoral added: “Every game is different, tonight we had to be a bit more secure defensively.
“We got it wrong against Parma but now we have to turn our attention to the game against Napoli.”
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