A second half substitute, the summer signing won a penalty to seemingly bring his side back into the game after Jose Luis Morales converted.
It was, however, not to be as the visitors held on to claim all three points on offer at Estadio Ciudad de Valencia.
It was Dwamena's second appearance for Levante since completing a four-year move from Swiss club FC Zurich earlier this month.
He has now been directly involved in two goals in two matches for his new club.
On his debut, the Ghanaian was introduced on the 90th minute mark but that did not stop him from grabbing a stoppage time assist in a 3-0 victory over Real Betis.
And on Monday, he made his presence felt again, this time after coming on in the 59th minute.
The 22-year-old was brought down by Sergio Alvarez as he tried to go round the goalkeeper, and referee Alejandro Hernandez had no hesitation about pointing to the spot.
Morales stepped up and neatly buried the kick to halve the deficit for the home side, Celta having taken a two-goal lead courtesy of strikes from Pione Sisto and Maximiliano Gomez.
The result has left Levante 10th on the table, three places below The Sky Blues.
Dwamena would hope to be rewarded with his first start when The Frogs host Valencia on matchday three on Sunday.