Birrell, who coached Ireland for four years from 2007 to 2011, said the non-Test playing nation had come a long way since his time with them.
"It's definitely not fair to kick them out," he said ahead of Tuesday's Pool B clash between South Africa and Ireland at the Manuka Oval in Canberra.
"Just look at their record. They've continually knocked down the door and they keep getting shut out.
"When I started in Ireland there was probably one or two players who were fully professional, now they're all professionals.
"They punch above their weight and I am not surprised at all. Every World Cup they seem to beat a full-member team."
Ireland knocked Pakistan out on their World Cup debut in 2007, defeated England four years later and have already beaten the West Indies in the ongoing tournament.
"They are a seriously good team and we are taking them very seriously," he said.
The Proteas go into Tuesday's match buoyed by the brutal 162 off 66 balls by de Villiers against the West Indies in Sydney last week that fashioned a 257-run win.
"I don't know if there is an attack in the world that can contain AB," said Birrell. "It's a matter of getting him out. If you don't he is going to hurt you.
"He is in a rich vein of form, but he is often in a rich vein of form. His stats over the past year have been phenomenal."
