The Republic's Euro 2012 nightmare was completed on Monday night when they lost 2-0 to Italy to become only the fourth country to exit a finals without picking up a single point.
The competition could mark the end of the road for the likes of Robbie Keane, Shay Given, Damien Duff and Richard Dunne.
But Andrews, who would become the oldest outfield player in the squad overnight were that quartet to hang up their boots, said: "The lads that are being talked about in particular have been fantastic servants - absolute stalwarts of the team of the last 10 or 12 years.
"On a personal note, I've really enjoyed playing with them so hopefully they don't go, but it's their decision."
Despite being 31, the 32-cap Andrews is a novice in international terms compared to Keane (120 caps), Given (125), Duff (100) and Dunne (76).
Regardless how many of them stay on, Ireland face a huge rebuilding job in the coming years, with many now questioning whether 73-year-old manager Giovanni Trapattoni is the man to oversee it.
Even if the Italian does stay in charge, the clamour for a change of approach is beginning to grow following a gruelling build-up to Euro 2012.
Andrews said: "Let's be frank, we haven't qualified for this tournament for 24 years.
"It is easy to sit there and criticise a man who got us the qualification.
"He's not really going to change something that's brought us a lot of success over the last four years, is he?
"We are not pleased with our individual performance, collective performance and, certainly, we've come up against fantastic opposition."
They included Spain and Croatia, who Ireland were comprehensively beaten by before salvaging a modicum of pride on Monday night.
They threatened to do more before Andrews was sent off for the softest of second yellow cards, the West Brom midfielder revealing he lost his cool following a number of "unfair" refereeing decisions.
But he admitted Ireland ultimately had only themselves to blame for their demise.
"We said before the tournament we wanted to give a good account of ourselves and there was no point coming for the craic," he said.
"To be perfectly frank, we simply weren't good enough."
Andrews faces suspension for Ireland's opening World Cup qualifier next season following his red card but he was not even thinking about another campaign.
"There's no chat like that," he said. "We are all bitterly disappointed, full stop. We need to regroup. Whoever is going to leave might leave.
"They will make up their own minds in their own time when they go back with their families and friends.
"The manager, I'm sure, will get a group together for the friendly in August going into the qualifiers in September."
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