The Reds are currently 13th in the Premier League table having beaten both Stoke City and Bournemouth by narrow margins, but come unstuck against Manchester United and West Ham and held by Norwich City and Arsenal.
They have been uninspiring, to say the least, with Tuesday night seeing them require a penalty shoot-out to see off League Two outfit Carlisle United in the Capital One Cup.
The pressure is firmly on Rodgers once again, with many tipping him for the sack, but Evans has urged the club to give the manager time to turn things around.
“He’s certainly under some serious pressure,” he told the Alan Brazil Sports Breakfast show.
“They’ve got to give him maybe just a little bit more time, it’s still very early in the season. You’ve let him spend an awful lot of money; you’ve got to give him a bit more time to see if it will work. Things can turn around in two or three games.”
Home form may be the root of the problem
A big concern for Rodgers and his side is their current home form, with the Reds winless in three games at Anfield.
Although they beat Bournemouth early on in the season, that was a narrow victory which should not have stood - while more recently, West Ham won comfortably there and Norwich earned a draw last Sunday.
And Evans believes that their struggles on Merseyside may be the root cause of their problems.
“Anfield doesn’t have that fear factor now,” he added.
“We’re letting people get their feet under the table. Years ago, right from the kick off we could win the game in the first 15 minutes but that doesn’t seem to be happening anymore.”