The striker had to be substituted after crashing into the post seconds after giving his side a 2-0 lead
The Spain international sustained the knock after colliding with the post immediately after scoring Atletico's second goal of the evening.
The 25-year-old left the pitch with a sizeable gash on his leg and was visibly in pain as he made way for Cristian Rodriguez, but the Vicente Calderon side were quick to downplay the significance of the injury.
"Fortunately, Diego Costa only has a wound after crashing into the upright," Atletico stated via Twitter.
"Costa is fine, he is happy. He has a cut, but it's not a big deal," added head coach Diego Simeone.
Costa had previously won a penalty having been fouled inside the area by Angel Lafita, but failed to find the net from 12 yards.
The striker made up for his mistake later in the game with his 26th league goal of the season, only to then be stretchered off.
Atletico returned to the summit of the Primera Division table following Sunday's away win, leaving them three points clear of second placed Real Madrid.