The Newcastle youngster was shown two yellow cards by referee Jon Moss, and his manager John Coleman was furious with the official who, he claimed, "couldn't wait to get the yellow card out to send him off."
Coleman has since apologised for his comments but insisted he stood by much of what he said. Barlaser was booked in the third minute and then dismissed in the 59th minute, leaving Accrington to play for over half an hour with ten men against a side from the division above them, and Martyn Waghorn scored a late winner for Derby.
Barlaser told Accrington's official website: "It's very hard to take. Obviously I am disappointed in myself in getting sent off and letting the team down but before that we had chances.
"I didn't watch it after I was sent off but apparently we had chances too and their goal was lucky. I would say the second yellow, okay, but the first one was the third minute so I don't know why he has given that. It's my first tackle.
"I can see why he has given the second one maybe but I feel the first one was harsh."
Liam Gibson wasn't involved for Accrington. Elsewhere in the FA Cup, Dwight Gayle was an unused substitute for West Bromwich Albion as they earned a replay against Brighton & Hove Albion with a goalless draw at the Amex Stadium.
In League One, Elias Sørensen watched from the bench as his new loan side Blackpool beat Coventry City 2-0 while Jamie Sterry completed his temporary switch to Crewe Alexandra minutes before their 2-1 home victory over Colchester, meaning the right-back wasn't able to play.
Jack Colback played the full game as Nottingham Forest beat Wigan Athletic 3-1 in the Championship. In Turkey, Henri Saivet appeared as a late substitute for Bursaspor in their 1-1 draw with Kayserispor.