The Cottagers play host to leaders and champions Manchester United on Saturday with the signs looking ominous for the Londoners having already conceded four to the Red Devils in the FA Cup earlier this month.
However, Hodgson, whose troops are currently eight points clear of the drop-zone in ninth position, remains confident his side can amass enough points from their remaining games.
"I will certainly feel very confident that this team we will not have any problems with relegation," Hodgson said.
Belief"I feel that we've played well enough all season and with nine matches left to play I can't see any reason why we can't play well in those nine matches and get some more points and try to maintain our position."
But the former Blackburn coach insists he will keep telling his players that they need to reach the hallowed 40 point mark before they can begin looking further up the table.
"I'm certainly not prepared to make categorical statements, until we get over that 40-point mark I'm going to say the same as every manager in my position - 'let's get to that 40 points first and maybe then we can start to really relax'.
"I think we've done well enough so far now we've broken this away hoodoo, I'd like to think that we can continue in the next nine games as we have done in the previous 29 and if we do that I don't have any fears for relegation."