However, he admits their difference of opinion could have been resolved long before it eventually was if the two men had not been so stubborn.
Pallister and Keane formed part of the bedrock upon which Sir Alex Ferguson's all-conquering United dynasty was built, but as his time at Old Trafford drew to a close - he returned to first club Middlesbrough in July 1998 - Pallister was at loggerheads with the combustible Irishman.
He said: "We just had a fall out on a pre-season tour
We ended up not speaking
It was weird
It wasn't like we hated each other
We were just both stubborn enough not to say, 'Here...'
We should have both put our hands out after that and got on with it.
"We laughed about it at the time, but we just wouldn't be the one to say, 'Let's forget about this'
That's how stubborn we were.
"But when I left to go to Middlesbrough, I went to get my stuff out of the dressing rooms at The Cliff and Roy was walking up the stairs as I was walking down
He started laughing, I started laughing.
"We shook hands and he said, 'I wish you all the best, big man' and we started talking again after that
Something as daft as that, two people being stubborn."
Pallister was speaking in Dublin, where Keane is currently helping Martin O'Neill to prepare his Republic of Ireland squad for Sunday's friendly against England, at the launch of Ford's exclusive '152' Summer Sales Event.
He added: "The last time I saw him was over at one of the Champions League games
He came to the hotel and we sat down for a coffee and a chat and a catch-up
He's good company.
"I admire Roy for the way he is and the fact he always speaks his mind
He's forthright in his views and says what he feels - whether that's always right or it's wrong, you've got to admire that."
United old boy Andrew Cole revealed during a visit to Ireland last year that he saw Pallister and Keane come to blows in Marbella on his first pre-season trip with the Red Devils, although the central defender played down the incident, which left the Irishman looking for his watch.
Pallister said with a smile: "That was a good night
His watch fell on the floor
He was more concerned about that
It must have been a very expensive one.
"It was handbags
It kind of happened on a players' night out
You hear things and things are said and I don't think there were any connections with any punches.
"But we managed to keep it quiet from the gaffer - that was always important."
For all that, Pallister retains a huge admiration for Keane and is confident he will return to management in his own right before long
He said: "I'm delighted to see him doing well - I'm delighted to see all the guys I played with who have gone into coaching or management do well
He evokes a lot of media coverage, does Roy.
"I got on great with him while I was at United
We had our ups and downs at times
I think he's a very strong character.
"I would expect to see him back in management in his own right eventually, but I think he will be very good for the Ireland team right now."
Source : PA
Source: PA