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."
Sevilla stay fifth on 45 points, one point short of Real Mallorca in the Champions League qualification places.
NEWS:Sevilla sack Jimenez
Leaders Real Madrid have 68 points and visit neighbours Getafe on Thursday. Barcelona and in-form Lionel Messi, who are second on goal difference, play host to Osasuna on Wednesday.
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Earlier, Deportivo La Coruna had two men sent off and conceded a goal deep into injury time to go down 2-1 at Sporting Gijon, suffering another blow to their fading Champions League aspirations.
They remain seventh in the standings with 42 points, behind Athletic Bilbao on goal difference.
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.
Depor rallied after the break and Adrian Lopez sprinted clear to level the north-coast derby only for defender Alberto Lopo to concede a disputed injury-time penalty.
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.
