Former Everton number two Irvine has helped North End climb away from the foot of the table, with a 2-2 draw at Plymouth Argyle ensuring their escape from the drop.
Shaw told the Lancashire Evening Telegraph: "For a club like ours relegation would have made things extremely difficult.
"The turnaround since the New Year has been nothing short of tremendous.
"I wouldn't say I have exactly been having sleepless nights over the prospect of us going down, but it has certainly caused us all a lot of concern.
"So full marks to Alan, his backroom staff and the players for turning things around so dramatically."