The Villans are currently in the relegation zone on goal difference with seven games left to play in the campaign.
"The Aston Villa fans are very worried at the moment but I have to say they've stuck behind their team," Taylor told talkSPORT.
"There are some of them who realise what Paul Lambert has come into. The money isn't available that was previously and he's now encouraging the young ones.
"I really do hope they stay in the division but I think it's going to be a hard job for them."
Villa continue their battle for survival on Saturday with a trip to Stoke City.