The Atletico Madrid striker the problem after being involved in an incident with his opposite number at Valencia, but assured fans that the damage was not too severe
The 26-year-old, who has been heavily linked with a move to Chelsea, failed to score for Los Colchoneros and was upstaged by Roberto Soldado, who did manage to find the net, as well as accidentally hurting his fellow striker.
Falcao stayed on the field of play at Mestalla after receiving medical attention and later posted a message on the social networking site to reassure worried supporters.
"War wounds, part of the job.....go ahead! (Who says I don't work hard for the points? Ha!)" the striker tweeted to his 1.3 million followers.
"We're working to be up there [in the league table]. Now [to] get some rest. Greetings all!"
Atletico resume their Europa League campaign away to Academica on Thursday evening.