Josh Scowen scored twice with Mason Holgate, Conor Hourihane and Sam Winnall also finding the net.
Rochdale had to play for most of the second period with 10 men after Joe Rafferty was shown a red card soon after the re-start after picking up his second booking for a foul on Scowen.
Johnson said: “I was pleased because it was the sort of pattern we are trying to play.
“We tried to give George Maris a free role on his full debut and there’s no better debut to have than being given a free role! I was delighted for him.
“We looked reasonably solid. They’ve got some good players and the sending off was a bit harsh, but we’ll take it because we’ve had a few bad decisions ourselves this year.
“The result sends everybody home happy. We’ve just got to be careful that we don’t think we’re better than we are, just because we’ve had a good 25 minutes at the back end of a game.
“Everybody wants to go home and think about what could be next year. We can believe that we’ve got a chance.
“We know there will be some changes and additions to the squad. It just goes to show that we’ve got a strong group if we can make six or seven really good additions.”
Rochdale assistant-manager Chris Beech said: “To be honest, I thought we were better than Barnsley after the red card. The two decisions leading to the set-plays for the first two goals changed the game more than the red card.
“We kept the ball very well, but Barnsley are one of the best teams in the division at scoring from set-plays. They have good delivery and good movement.
“Once they were two goals in front, it was very difficult to claw back so the game ran away from us.
“We’ve got a great young squad that’s gone through a two-and-a-half-year development. I don’t think there’s too much in terms of pulling apart something that’s obviously very good.
“To finish eighth in League One is the highest the club has ever finished so that is something to hold onto going into the summer.”