Defeats against Arsenal, Manchester City and Wigan mean Andre Villas-Boas' men could be languishing in mid-table by tomorrow night if they put in another disappointing display against the in-form Hammers.
Tottenham have lacked the cutting edge that won them two top-four places in the last three years and have looked shaky in defence on several occasions this season.
Adebayor cut a remarkably pessimistic figure as he trudged out of the Stadio Olimpico last night after Spurs' fortuitous 0-0 draw against Lazio, and urged his team-mates to up their game.
"We're all frustrated about the way things are going," he said.
"I don't know what's not clicking. Hopefully it will start clicking as soon as possible otherwise, trust me, we will find ourselves in difficulty.
"My friends tell me to keep positive so I don't really want to think about how bad it could be. If we get badder (sic) than this, I think we'd be dead.
"It was our lucky day against Lazio. They got so many chances.
"At the moment things are looking bad, but we just have to find a way to get through this. We have to improve because we're not playing the best game at the moment."