Bayliss told BBC Radio Cumbria, "I think some supporters have been spoilt on the success we've had.
"But I've got no doubt that they are right behind the team and will back us all the way."
The Bluebirds lie 18th in the Blue Square Premier, three points above the relegation places with three games left to play.
I think you learn more about yourself and your players when you are getting beat
Dave Bayliss
"We need everyone to be pulling in the same direction."
"The support has been a different class home and away this season bar one or two but you get that in football. The true Barrow supporters will be behind the lads.
"We're up against teams who have wage bills of up to £1million a year. Ours is nowhere near that but we're competing really well."
emp_load.getEmpEmbeddedParams("emp_7999648");Bayliss also said that both he and fellow manager Darren Sheridan had learnt a lot over the course of this season following their appointment in November 2007.
"I think you learn more about yourself and your players when you are getting beat.
"It's made me realise how much you need men in your team like Paul Jones. If we had eleven Paul Jones' in the team then we wouldn't be far off a mid-table place." he added.
The Bluebirds could all-but mathematically secure their Blue Square Premier status on Saturday if they beat Crawley and Weymouth and Woking both lose.
"We can go into these big games now a little more relaxed.
"Our lads love playing in front of our own supporters because they are so passionate. We've got three games to go and we need the fans behind us now."
Source: BBC Sport
Source: BBC Sport