Suarez is free to play for the club until an appeal is heard and his team mates showed they were fully behind the striker when they all wore T-shirts emblazoned with his picture before the Premier League match at Wigan Athletic on Wednesday.
"He was quite emotional and very grateful," Dalglish told reporters at Liverpool's training ground on Friday as they prepare for a hectic holiday fixture list.
"I don't think it's ever a disappointment when your team-mates and the people you work for give you their undivided support. For me, that's the least he deserves."
Liverpool are waiting for full documentation of the case from the Football Association and Dalglish was reluctant to go into detail about what it might contain.
The club was criticised by anti-racist organisations and some former players on Thursday for their stance over Suarez, but Dalglish said his players had done nothing wrong.
"We've certainly said what we have to say. We'll wait until we get the judgement and take it from there," Dalglish said.
"The players have made their statement both visually and verbally. It's best for everybody to wait and see what the written retort is because nobody knows - we don't even know.
"At this moment in time the club aren't permitted to go into any further detail than what they have done in their statement, which couldn't have caused anyone any trouble.
"I don't think the players have caused any trouble with the FA either with their statement or the T-shirts, so if we're not in any trouble we'll just leave it at that before we do give ourselves some trouble."
Liverpool face Dalglish's former club Blackburn Rovers on December 26 with the Scot offering some sympathy to Rovers' beleaguered boss Steve Kean who has come under fire with his side propping up the table.
"The most sympathy I have is for Blackburn because I was there for three or four years," said Dalglish, who led Rovers to the Premier League title in 1995.
"It was a great place for me to go and work, there were some smashing people there that were in charge of the club at that particular moment in time, and I would never have anticipated or foreseen the situation they are in at this particular moment.
"Blackburn are at the wrong end of the table, they are under a bit of pressure and there seems to be a bit of animosity in and around the club at the moment.
"Results aren't purely to what the manager does. You need support from your players, you need support from the owners and you certainly need some support from the crowd."
