Karanka was interviewed as a potential Palace boss after the dismissal of Ian Holloway, but Parish opted to place Tony Pulis in charge, despite being impressed by the former Real Madrid man.
It was a decision which Middlesbrough will be very grateful for, as they have progressed hugely under Karanka, and that is something which has not come as a shock to Parish.
"I had a chat with Aitor Karanka before he went to Middlesbrough and he was very impressive," he said. "I just thought by the time he arrives, unpacks his bags, gets his house sorted and works out who players are...
"It's not like a squad where you'd know all the players at that point, and we'd lose four games and then there's pressure on you again."
The decision of Parish to pick Pulis is impossible to criticise, as it worked out so well for the Eagles, but Karanka also would have been a good appointment.
Pulis did brilliantly at Palace, helping them climb the Premier League table at a staggering rate, but he has since departed.
Karanka, meanwhile, has made steady progress with Middlesbrough - creating a continental approach at the Riverside which is proving to be very effective.
Boro are now amongst the leading candidates for promotion from the Championship, and Karanka could well get the chance to manage at Selhurst Park next season, even if it is not in the home side's dugout.