Spurs endured their third defeat to the Hammers in all competitions this season courtesy of a Harry Kane own goal and Stewart Downing free-kick.
The visitors saw Younes Kaboul shown a straight red card for felling Downing as the last man on 25 minutes, but showed an alarming lack of fight as West Ham comfortably wrapped up their first victory in a month.
After the match Sherwood remained bullish on his credentials to remain Tottenham manager beyond the summer, despite the club's apparent public courtship of Ajax boss Frank de Boer.
"If Tottenham don't know, two games before the end of the season, if I'm good enough to stay we've got a serious problem," Sherwood told BT Sport.
The Spurs boss also refused to criticise his team's performance in a match he insisted turned entirely on the dismissal of Kaboul on 25 minutes.
When asked if he thought his team had been out-thought, Sherwood told reporters: "I don’t think so. The game changed on the red card. Before that we were comfortable and had the best chance of the game.
"This was always going to be a tough place to come and when we went down to 10 men and they scored a minute afterwards, it was a difficult afternoon.
"The free-kick went straight through the middle of our wall, which wasn’t ideal, and then we had a mountain to climb."
In spite of the decision's significance, Sherwood insisted he had no complaints about the red card.
"It was the right decision," he admitted. "I don’t think Michael was getting round enough, so no complaints. But when you do go down to 10 men, it is very difficult.
"Credit to the boys, I thought we took the game to West Ham with 10 men and created a few half-chances. If we’d have taken one of them it might have been an edgy afternoon, but I’m not too displeased with the performance."
Sherwood also refused to blame Paulinho or Emmanuel Adebayor for parting to allow Downing's free-kick to fly through the Tottenham wall and beat Lloris at his near post.
"It wasn’t great but I spoke to them," he added. "I pointed it out to them but they don’t need me to point it out, they know it’s an error. It hurts a lot more when it leads to 2-0."