The 25-year-old told the club website: "I went in straight after the game to the referee and the gaffer to say sorry for my actions.
"I knew immediately that what I did was wrong," he added.
"What happened was out of character for me and I wanted to apologise for doing what I did."
Barnett is set to sign a three-and-a-half-year deal at Carrow RoadBarnett will now miss the weekend trip to Coventry but will have to wait to see whether the Football Association takes any further action against the centre-half, who is set to turn his loan switch from West Brom into a permanent move in January.
Meanwhile midfielder Simon Lappin, who has been filling in at left-back recently, says the team were frustrated by their defeat by Pompey.
Despite creating a number of chances, the Canaries failed to find the back of the net at Carrow Road.
Lappin told BBC Radio Norfolk: "Frustrated is an understatement. We've been excellent but if you don't take your chances, things can come back to haunt you."
Despite the defeat, Norwich remain sixth in the Championship table, eight points behind leaders QPR.
As long as we keep playing like that we've got nothing to worry about, we'll go to Coventry next week and play the same way
Norwich City midfielder Simon Lappin
"You just think it's one of those days," said Lappin playing left-back due to injuries to Adam Drury and Steven Smith.
"The manager has asked me to play there and I'll do it to the best of my ability. I give it my all no matter where I'm playing - I always do.
"As long as we keep playing like that we've got nothing to worry about. We'll go to Coventry next week and play the same way."
Grant Holt will be available after serving his one-match ban but Norwich could be in more defensive trouble if Lappin receives another caution: he is already on four for the season, one short of a one-match ban.
"You cant think about it. If you do it might take away a bit of your edge. It's part and parcel of football," he said.
Source: BBC Sport
Source: BBC Sport