The Reds were paired with the Toffees at Oakwell after Johnson's side overcame Scunthorpe in the First Round on penalties.
"It's a fantastic draw for us," said Johnson, speaking to barnsleyfc.co.uk. "You couldn't have picked a better draw, I don't think.
"The game is a brilliant opportunity for us to test ourselves against an excellent Everton side. I'm sure the lads are all pleased with the draw and they'll be buzzing to get stuck into the tie.
"We will certainly have to be at our best but the lads won't need any motivating as they'll want to test themselves against some of the world's best players.
"I'm sure the Reds fans will back us in their numbers and there will be plenty of bums on seats for what really is an excellent tie."
