Slot finished just three points ahead of Bournemouth in the top flight this season failing to win a trophy, despite lifting the league title in his first campaign.
Liverpool wasted no time in replacing the Dutchman, bringing in Iraola who many will hope can implement a more aggressive and implement a front-footed style much like former manager Jurgen Klopp.
However, despite many being over the moon with the appointment, Barnes spoke to Betfred about how Liverpool need to be careful or they could fall into the trap of constantly sacking head coaches.
“That’s modern football. The owners, the chief exec and the rest of the hierarchy don’t sack managers, the fans do.
"If the fans lose faith in you, then unfortunately for all managers, this decision has to be taken. I’m sure they (the Liverpool owners) wouldn't have wanted to do it but it’s the fans that decided and that’s unfair in my opinion.
“If Iraola comes in now and loses a few games, are they going to sack him? And then sack the next manager?
"I support the club and the decisions they make, but I’m hoping the fans will have a lot more patience with the next manager.
“We don’t want to go down the route that Manchester United have been down. Mikel Arteta finished eighth, eighth and then fifth (at Arsenal) and his club didn’t sack him and look where they are now?
“Liverpool fans need to be careful what they wish for.”
During the second half of the season, Iraola led Bournemouth to an 18 game unbeaten run, sixth-place finish and Europa League football as they enter Europe for the first time in club history. Iraola has signed a two-year deal at Anfield and as the summer approaches, supporters will be eager to see how he changes the side.