Jake Jervis sealed victory for Pompey with the only goal after 48 minutes when he cut inside from the left and lashed a low drive into the bottom corner of the net.
Barker made five changes as the hosts bounced back from their 5-1 battering at Scunthorpe on Saturday with a far more spirited display.
He said: "I felt we needed to send out a message to people. We've set ourselves some high standards over the last few weeks and it was important that if we let them drop, we didn't accept it.
"It was important that people recognised if they didn't do what they had been asked to do, they're not going to keep their place in the team for very long.
"We've got a strong squad, we've got options and I think we showed that by making five changes and winning the game.
"The pleasing thing for me was the attitude and the clean sheet. We probably should have won by another goal, to be honest, and made it a little more comfortable than it was."