The Uruguay international was on the end of a number of challenges which failed to earn free-kicks during Monday's 1-0 defeat at Fulham.
Suarez left the field frustrated and is alleged to have made an offensive gesture to the crowd at the final whistle, which has resulted in a Football Association improper conduct charge.
It is the 24-year-old's second brush with the English authorities this season as he is still awaiting a date for his hearing to put his defence against a charge he racially abused Manchester United defender Patrice Evra in October.
Dalglish said: "People find it difficult to play against him. If they cannot beat him on the pitch because of his ability, they will try to get into people's minds - and that's what they try to do.
"The people that have any favour towards Liverpool Football Club will get right behind Luis Suarez and give him all of the support he deserves. We are lucky that he is a fantastic footballer, one every other club would love to have in their side, and he is playing for us so we'll help him as much as he can."