Suarez has been handed a four-month ban from all football-related activities, in addition to a nine-match international suspension, after biting Italy defender Giorgio Chiellini when representing Uruguay at the World Cup in Brazil.
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However, Dalglish expects Liverpool to remain steadfast in their support of the 27-year-old, who has now been found guilty of biting on three occasions.
Writing in the Daily Mirror, the former Liverpool player and manager said: "I know that lots of people are jumping up and down and saying that Liverpool should disown Luis Suarez.
"Others are saying that the striker has become more trouble than he is worth, too. But you don't just turn your back on someone because he has done something wrong.
"I think you will find that Liverpool will not turn their back on Suarez, whatever the ban Fifa have decided he must serve."
Dalglish also questioned the consistency of the bans handed out to Suarez, with the player's previous suspension for biting Ivanovic not preventing him from playing for Uruguay.
"When he was punished by the FA for the biting incident with Branislav Ivanovic and banned from domestic games, he was still allowed to play for his national team," Dalglish added.
"It seems a bit strange, then, that when he is banned for something he did with his national team, his club has to suffer, too."