Giovanni Trapattoni's side lost all of their Group C games in convincing fashion after being outclassed by Croatia, Spain and Italy.
The former West Brom midfielder feels the negative comments the side have come in for are harsh, considering their recent record in qualifying for major tournaments.
"It is very hard to face this criticism because, let's be honest, we haven't qualified for this tournament for 24 years and criticising the man who got us up here is not really fair after the four years we had," he told reporters.
Andrews was sent off in Ireland's 2-0 defeat to the Italians for two bookable offences and reacted furiously after he was given his marching orders, gesturing towards Turkish referee Cuneyt Cakιr and lashing out with his feet on his way off the field.
But the 31-year-old claimed he did not speak to the official on his way off the pitch and that he was simply disappointed with the decision.
"I never said anything to the referee on my way off, [it was] pure frustration," he added.
The international future of veteran players such as Robbie Keane, Damien Duff and Shay Given has been questioned throughout the tournament, with many believed to be considering retirement. However, Andrews stated no decisions have yet been made.
"I think all the lads will make up their own minds when they are back in their homes with their families and friends and then we will see where we stand," he said.
"There was no chat afterwards about what comes up next, with the World Cup qualifiers. Just disappointment, full stop."
Andrews was pleased with the character shown by his side and believes they coped well with the Azzurri in open play. Indeed, Antonio Cassano and Mario Balotelli scored the two goals from set-pieces, one of Ireland's traditional strengths.
"There was a spirit in our performance of course, we started brightly each half. They were under pressure though they obviously kept the ball pretty well," he added.
"We tried to squeeze them, press, and play in more narrow formation. Then comes the set-piece, the smallest player on the pitch... it's been a killer in this championship, hasn't it?"