Lerma accused Aspas of making a racial slur during Celta Vigo's 1-0 away win, and said he reported the incident to referee Alfonso Alvarez during the match.
Levante later issued a brief statement on Twitter supporting its player, which read: "Following the statements of Jefferson Lerma at the end of #LevanteCelta, Levante wants to show its firm support to the player and rejects any sign of racism in football."
Aspas – who played the full 90 minutes – responded to the claims via Celta's official website.
"What is said on the field, stays on the field," he said. "So I will not repeat what he said to me.
"In any case, I did not call him what he attributed to me."
Accompanying Aspas's denial was a brief statement from Celta that said the club "strongly defend fair play and respect on and off the pitch."