The City boss was spotted with the scratch during Tuesday's 3-3 draw at the Etihad, in which they blew a 3-0 lead, and was asked about it during his post-match press conference.
Guardiola replied that he had caused it with a fingernail, adding apparently as a joke: "I want to harm myself."
City went into the game on the back of five straight defeats in all competitions.
Guardiola held his head in his hands in the dugout after a Josko Gvardiol blunder gifted the first Feyenoord goal to Anis Hadj Moussa.
The Spaniard took to social media to clarify his response on Wednesday, saying: "I was caught off guard with a question at the end of a press conference last night about a scratch which had appeared on my face and explained that a sharp fingernail had accidentally caused this.
"My answer was in no way intended to make light of the very serious issue of self harm.
"I know that many people struggle with mental health issues every day, and I would like to take this moment to highlight one of the ways in people can seek help, by calling the Samaritans hotline on 116 123 or emailing jo@samaritans.org."
