The 61-year-old was sacked after a disappointing Premier League campaign which saw the Reds finish in eighth place, 37 points behind champions Manchester City.
Speaking at Thursday 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.
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"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."
Luis Suarez has thanked the former Liverpool manager for his support and wished him luck for the future on his Twitter page.
The forward wrote: "KENNY thank you very much for all your help and things I learned from you during 1 year and a half! A big hug and good luck!!"