Sam Allardyce's side enjoyed a remarkable start to the campaign, sitting as high as fourth after 17 matches to spark talk of qualifying for Europe.
But the subsequent 16 games have yielded only 12 points to leave West Ham 10th ahead of Saturday's trip to relegation-threatened London rivals QPR.
"Our dressing room is fired up," Jenkinson, on loan from Arsenal, told West Ham's official website. "If you go in the dressing room after the game people aren't resting on their laurels, people aren't happy finishing mid-table.
"We want to kick on, we've got things to prove because we've been on a bad run recently and we want to put that right for us and the fans.
"We want to finish as high up the league table as possible. After the start we had we're not just going to accept a mid-table finish."
