The striker was given a four-month suspension from all football activity, as well as a nine-match international ban, for biting Italian defender Giorgio Chiellini in a World Cup game last Tuesday.
It is the third time the 27-year-old has been punished for such an offence and it has led to calls for Liverpool to cut their losses on the player, who they will be without for the first nine Premier League and three Champions League games of next season.
However, former Reds player and manager Dalglish, who brought Suarez to Anfield from Ajax in January 2011 during his second spell in charge, believes the club will support the player, who he feels needs help to control his emotions.
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 you 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 also feels the punishment handed to Suarez, who scored 31 goals in 33 matches last season, is harsh on Liverpool.
"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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