Deila has come under pressure in recent weeks due to disappointing results in the Scottish Premiership and in the Europa League.
The Bhoys, who failed to progress to the group stage of the Champions League at the start of the season, could not qualify for the knockout rounds of the Europa League.
Last weekend, the Hoops suffered a surprise 2-1 defeat to Motherwell at Celtic Park in the Scottish Premiership.
Celtic fans are not happy with Deila and many want him sacked. Hay, a former Celtic midfielder and manager, believes that the Norwegian should not pay too much attention to his online critics.
“Just this week, a petition was put online by some supporters demanding Deila be sacked by Celtic,” the former Scotland international has written in The Glasgow Evening Times. “That’s life as a high-profile football manager in 2015.
“Everyone has a point and everyone has a chance to make that point. My advice to Deila is not to go online at all. No good could come off it.
"If the guy absorbed every word and listened to every call-in show then he wouldn’t get out of his bed in the morning. But I do understand why a lot of the Celtic support is so frustrated.”
Celtic will return to Scottish Premiership action on Sunday afternoon when they take on Heart of Midlothian away from home at the Tynecastle Stadium in Edinburgh.