Carragher, one of Britain's best-known football pundits, has been suspended by Sky after footage emerged of him spitting through his car window at a 14-year-old girl who was goading him about Liverpool's 2-1 defeat at Manchester United.
Opening his Drivetime show with Saira Khan, Eamonn said, he would have expected far sterner punsihment than a dismissal.
"If I'd been filmed 'gobbing', with a massive amount of spit in my mouth, at anyone, let alone a 14-year-old girl, I can tell you I would not be on air here today," Eamonn said.
"I would have been suspended and I certainly wouldn't expect to be on television again."
Saira said the treatment of celebrities who transgress is simply "one rule for one and another for another."
She added that the incident is particularly galling because, as a footballer, "aggro and a bit of banter is a part of your make-up. You're surely taught to hold yourself, ignore it, move on."
When asked what Sky will do about Carragher long-term, Eamonn said "Sky only care about Sky. Sky realise he's good box office, he's great business, and I'd be very surprised [if he was dimissed].
"I think they're going through the old moral wringing their hands, putting him on new shows, Jamie's apologised very, very well - as he should.
"But if it was Piers Morgan, if it was Ant and Dec...."
Watch the clip below.