Giovanni Trapattoni's hopes of guiding Ireland to a second successive tournament finals were dealt a huge blow on Friday night when they lost 2-1 to Sweden in Dublin.
The defeat proved the final straw for many fans, who are desperate for the 74-year-old Italian to go before his contract expires in June next year.
Martin O'Neill, the man Quinn appointed as Sunderland manager in December 2011, is the bookmakers' favourite to succeed Trapattoni, but the former Ireland international striker believes more fundamental issues need to be addressed.
He said: "Money has to go into an elite academy. There needs to be a six-year programme put in place to get Ireland back up to the levels of 20 years ago, to when we could and did compete.
"At the moment, there's a reliance on getting into the top Premier League clubs, but it's just not happening.
"The pool is so much smaller, so we have to deliver change ourselves. We have to make sure our players are better equipped and in better shape if and when they move to England.
"When Trapattoni started, he had Shay Given, Robbie, Damien, Richard Dunne and John O'Shea, players of real quality, and all of them at the peak of their careers.
"The next manager won't and in some ways will be snookered before the off. If anybody thinks our problems will be solved simply by the appointment of a new man, then they need their heads examined.
"The reality is that we should expect a long time in the wilderness if we don't realise that we have to prepare young players better for top-flight clubs, players who can hold their own in England.
"There needs to be a long-term plan and I would like to see the appointment of the next manager reflect that, to be someone who will buy into that and to be given time, without the threat of the sack."
Trapattoni's Ireland only just missed out on qualification for the 2010 World Cup finals when they went out at the hands - literally in Thierry Henry's case - of France after a controversial play-off.
They did make it to Euro 2012 in Poland and Ukraine, but returned swiftly without collecting a point from their three group games.
Given and Duff have since retired from international football and a new generation of players, including Seamus Coleman, James McCarthy and James McClean, has been blooded.
However, qualification for next summer's World Cup finals in Brazil looks a remote possibility with just three games remaining, and Trapattoni's critics are growing in both number and volume by the day.
- Sports & Recreation
- Giovanni Trapattoni
- Damien Duff
- Robbie Keane