The midfielder was given his marching orders for a reckless challenge on Liam Bridcutt on the stroke of half-time, with Henry now facing a three-match ban and his second suspension of the season.
In stark contrast to Brighton's late penalty, Solbakken felt the decision to show his captain red was correct. He said: "Karl made a big mistake there. He knows that. He knows it was a bad challenge.
"We shot ourselves in the foot twice at the end of the first half with the red card and the goal we conceded, and going in at 1-1 with 10 men gave us a mountain to climb. But we showed in the second half that we are very well organised.
"Some errors cost us in the end but the important thing is that we stayed united, and it was good for the fans to see the team come back and show character."