Dalglish saw his contract terminated by Liverpool on Wednesday following a disappointing Premier League season in charge of the Reds, as the club finished in eighth place.
Speculation has already begun over who will replace the coach at the helm - with former Chelsea boss Andre Villas-Boas the current bookmakers' favourite.
Carragher has admitted to his disappointment at seeing the club legend part ways with the Anfield side, but trusts the owners to make the right appointment.
Speaking at this morning's ITV Sport Euro 2012 launch in central London, Carragher said: "I spoke to him just before he was getting on his flight and asked: 'is it Kenny now or gaffer?'. He said 'it is Kenny now'.
"I am sorry to see him go, but that is football. It is a sad day for him, but we respect the owners' decision and we have to look forward now. I will be fully committed to whoever the manager is."