Valladolid, who were promoted to Spain's top flight for the beginning of the 2012-13 season, were sent back down to the Segunda Division after they were beaten 1-0 at home to Granada.
The result, which secured Granada's Liga status, saw Valladolid relegated alongside Osasuna and Real Betis.
Speaking after the match, Martinez apologised for failing to avoid the drop.
"I apologise to the club and the fans, because I didn't fulfil the task I was trusted with, after I came here last summer," said the 49-year-old.
"Obviously I'm the one with the utmost responsibility and for that, I apologise."
Martinez also admitted he was unsure whether he would be at the helm next season: "The sporting director will meet next week with the players and coaching staff. From there, he’ll inform us of his decisions."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.