The Saddlers were comfortably beaten by promotion-chasing Wigan on Wednesday, a result which leaves them sitting just four points above the drop zone in League One.
That defeat – in Dean Keates’ first game as boss – was Walsall’s fifth loss in their last six outings.
But while Chambers accepts his team are now in a fight for survival, he believes it’s important everyone remains calm.
“We have to realise the situation we are in but it is important not to panic,” the 37-year-old said.
“Each game now is going to be big. We have to look to win each one.
“It is going to be about hard work and replicating what we do on the training pitches come match day.
“We have to go into each and every game looking to win. That has to be our focus.”
After replacing the sacked Jon Whitney last Friday, Keates opted to watch the Wigan game from the directors’ box instead of being in the dugout.
He was involved in selecting the team, while he also addressed players in the dressing room before and after the game.
But Chambers feels it’s not until the Saddlers take on Portsmouth a week tomorrow that fans will really see the impact of the new boss.
“It’s very early, he (Keates) has only been in a couple of days,” the midfielder said.
“He has been watching and keeping an eye on things.
“He will now start to put his points across more and tell us what he expects.
“When you are just through the door, it’s difficult to get your points across.
“Now we all need to move forward under the new manager.”
Walsall’s next two games – against Pompey and Bradford – are against teams that still retain an outside chance of finishing in the play-offs.
But after that, the Saddlers face Bury, Oldham and Wimbledon – three teams who are also battling against the drop.
And Chambers admits the team has got a big few weeks ahead.
“We’ve got some big games coming up,” the skipper added.
“We’ve been inconsistent. At times we have shown what we are capable of.
“We know it is in there. It is up to us to repeat that.
“It is up to us to prepare right, make sure we put in the hard work.
“We have to give our all to try and win each game. Hopefully, that will be enough.”