Costa proved the matchwinner at Champions League rivals Lokomotiv Moscow this week.
Lucescu, who coached Costa at Shakhtar, said: “Douglas Costa, in terms of quality, has no reason to envy Mbappe at PSG.
“The other day he scored a beautiful goal in the Champions League, but he's got the quality to score goals like that every game.
“Trust me, I know," added the 74-year-old, who brought the Brazilian to Europe during his successful tenure at Shakhtar."
He added, “He's a very generous player, he prefers to make an assist than score himself."