Andrews was part of the Republic of Ireland team controversially defeated in the World Cup play-off by France in Paris while Ryan Nelsen captained New Zealand in their historic victory over Bahrain which sealed only his country's second-ever finals place.
"It is total opposites," said Allardyce, ahead of the Lancashire derby.
"Ryan has a big smile on his face and was bouncing in through the door after the achievements of getting to the World Cup finals for the first time since 1982.
"His euphoria will hopefully be rubbing off on everybody else to go and give a gigantic performance at Bolton on Sunday.
"The opposite end is the unfortunate situation that Keith Andrews found himself in - on the wrong end of a defeat that wasn't deserved and decided by a very controversial decision.
"It is very difficult to get over but he must get over it and get on with playing for Blackburn Rovers. I have every sympathy for him and everyone concerned with the Ireland team."
Allardyce will judge whether Andrews is both psychologically and physically fit to start at the Reebok Stadium after playing all 120 minutes on Wednesday night.
"Keith's face afterwards told the whole story," Allardyce continued.
"He couldn't hold back the tears any more and he was totally and utterly distraught, as everyone connected with Ireland would be.
"Knowing Keith he will be available for selection and wanting to play but we have to assess the overall fatigue, physically as well as mentally, and decide whether or not to select him on Sunday or not."
Nelsen, meanwhile, has been in celebratory mood since completing the two-day journey back from Wellington.
"It has been pretty crazy for the past few days," Nelsen said.
"The game electrified the whole country and it delivered. It was really entertaining and you could not have scripted it any more perfectly for the public.
"People are saying it is the greatest sporting event in New Zealand's history, in terms of a spectacle, and they can't get enough of it. "We punched above our weight to beat these guys. They are so well funded, have had many games together and we turned up and rolled them."
Blackburn already have bragging rights over traditional foes Burnley following a 3-2 victory at Ewood Park but a second win over local rivals would be more significant for their season.
Rovers have lost their last 10 away matches in the Barclays Premier League, conceding an astonishing 32 goals in the process.
So breaking that hoodoo is paramount in their bid to avoid another relegation scrap.
"We have had one big local derby against Burnley but over the years this has been equally as big as that one," said Allardyce, in his 12th month in charge, having previously managed Wanderers between 1999 and 2007.
"There have been more of the Bolton-Blackburn derbies and for many years I have been at the other end, both as a player and manager.
"As a Blackburn manager it is strange but I am looking forward to it and we must make sure we put our away form right."
Meanwhile, Allardyce has backed midfielder Steven Reid's decision to seek more first-team action with a one-month loan move to QPR.
"I was right behind him because I think consistent games is the one thing that Steven is missing," Allardyce said of Reid, who is out of contract at the end of the season.
"He will decide his own fate by hopefully coming back from QPR and then going back into Blackburn Rovers' team and being the Steven Reid of old."
Bolton 11/10, Draw 12/5, Blackburn 5/2