FORMER Ireland captain Matt Holland says it was the right time for Giovanni Trapattoni to step down because Ireland had underperformed during his five-year reign.
"I think it is (right)," he said. "The style of play was what frustrated the Ireland supporters because he is pragmatic and defensive-minded.
"We have better players than the way we performed."
But he added: "We should pay tribute to what he achieved and he has done an excellent job.
Holland won 49 caps for Ireland between 1999 and 2006 and added: "Let's not feel sorry for him. He's 74 years of age and has had a great career. Look at his achievements, he's won everything in the game.
"But everything comes to an end."
"The big favourite is Martin O'Neill, he's the one everyone is talking about," Holland said.
"He's out of a job and very much in the running. Brian McDermott at Leeds has potential."
On McCarthy he added: "He's doing a good job at Ipswich and I'm not sure he'd be too keen, but why not?
"Mick had great success so why not? A number would fancy it because we've got some very good players."
Defeats to Sweden and Austria left the Italian's team with no realistic hope of qualifying for the World Cup.
"I'm not really that surprised after the two results we had because we all knew this month was crucial for qualification," Staunton said.
"We were never going to qualify automatically, but I think everybody had hope and vision that we would come second and get a play-off, and it's a bit of a lottery then, but that's not going to be the case."
Staunton played during Ireland’s heyday under Jack Charlton, and the Englishman's success with the Republic has raised the country's expectations of success on a European and world level.
"We're always expected to qualify ever since Jack's era," Staunton said.
"Expectations have to be managed and controlled but sometimes they are unrealistic.
"Unfortunately things didn't work out. The criticism is coming from the tactics this time.
"But you can only work with the players you've got and unfortunately our players at this moment in time - we haven't got the biggest pool in the world."
There were calls for Trapattoni to go then, but he survived that and Staunton said "maybe he deserved another chance" for guiding the team to the tournament.
Staunton would welcome former Northern Ireland international O'Neill coming in to succeed Trapattoni.
"He's got more experience than anybody out there so it wouldn't be a bad shout," Staunton said.
"He's managed Celtic for five years and done really well up there, and at other clubs he's done really well, so that wouldn't be a bad choice. Who knows what the FAI have in mind, but Martin would be up there high on the list.
"I would like to see an Irishman get it or somebody who's from these islands, who knows what the Irish boys are about and knows the mentality. The FAI has a tough job now."