Leandro Gioda's deflected shot after a long throw-in cancelled out Frederic Kanoute's 63rd-minute penalty, and led to a barrage of whistles from the home fans when the game finished soon after at the Sanchez Pizjuan.
It was a lame performance from the King's Cup finalists who still appear to suffering a hangover from their surprise Champions League exit to CSKA Moscow last week, and who have now failed to win in seven attempts in all competitions.
When asked if he thought his position was under threat, Jimenez was bullish with reporters: "Results will be my judge. All this isn't new. They said the same last year.
"If we win the Cup and finish third the results will be better than we achieved last year."
The visitors had goalkeeper Daniel Aranzubia sent off after only 11 minutes at the Molinon, for tripping Mate Bilic outside the area, and Sporting's Croatian striker put the hosts in front with an opportunist strike in the 30th minute.
Lopo was sent off and Diego Castro struck Sporting's winner from the spot. Faltering Depor have only won once in their last five outings.
