They have not scored for six away games and their run-in looks tougher than their relegation rivals. They are level on 22 points with Queens Park Rangers and Burnley who are above them.
"I am ramping up the pressure on them. I am telling them 'We can't drop any more points.' Let's take it upon ourselves," Sherwood told reporters.
"Managers try and take the pressure off. I think Paul Lambert's probably been trying to do that to the guys all season. I'm going to try the other way. I'm going to put it on them."
The only bright spot so far under former Tottenham Hotspur boss Sherwood was a 2-1 FA Cup fifth round win over Leicester City, but the manager was not in the dugout for that game having only just been appointed.
The famous Birmingham club is in turmoil on and off the pitch, with American owner Randy Lerner looking to sell, and Sherwood thinks it is time the players rolled their sleeves up.
"People talk about 'Teams are too good to go down.' It's all nonsense. You have to prove it on the pitch. You have to go out there and do it," said the captain of Blackburn Rovers' 1995 Premier League-winning squad.
"We're under pressure boys. This is a massive football club with a lot of good people involved in it. The fans are magnificent. I think it's time we turn the pressure valves up already.
"But I saw signs today. This team is not ready to give up. There is plenty of time left."
(Writing by Mark Meadows; Editing by Ken Ferris)
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