The Uruguayan was given a four-month ban by FIFA from carrying out any football-related activities after biting Italy defender Giorgio Chiellini in their World Cup clash earlier this week.
It is the third time Suarez has been suspended for biting an opponent and Liverpool have faced calls to cut their losses with the controversial striker, despite his outstanding campaign for the Reds last season, when he scored 31 Premier League goals in 33 matches.
Yet Dalglish, who brought Suarez to Anfield from Ajax in January 2011, thinks more understanding needs to be shown to the 27-year-old.
The Scot said in his Daily Mirror column: "It is my belief that when you bring a player to a football club, he becomes your responsibility. You don't just turn your back on a player 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. Of course it will be a heavy blow if the club has to do without him for the opening months of the season.
"You can't really ask any one person why what happened against Italy happened, because there is only person who knows and that is Luis - some people have injuries you can't see.
"Sometimes, when people have something wrong with them, just because they don't have a plaster cast on their leg, people think they don't need help."
Dalglish was Liverpool manager when Suarez received an eight-match ban for abusing Patrice Evra. The squad warmed up wearing shirts bearing Suarez's name and image, and Dalglish described it at the time as "the least he deserves".
Now he thinks the new punishment is harsh on Liverpool as the incident was out of their control.
"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," he 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."
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