However, the Wolves board were clearly unimpressed with the result and later made the decision to sack the Norwegian.
The Hatters prevailed 1-0 at Kenilworth Road to leave Solbakken with just three wins from his last 17 games in charge.
"There will be a lot of questions over me but that is normal," he said after the game. "That's football and I have to take that, it's no problem. I can put it right.
"I'm not embarrassed by the result and I can't fault the players' effort. First half we did well, but second half we didn't, because our physical presence in the box was not enough.
"We should have been two goals up in the first half. We had two clear chances which we failed to take and, when they scored with their first or second attack of the second half, we struggled to come back.
"They protected their penalty area very well. They overcrowded it in the second half and we didn't manage to win those battles. We tried to put crosses in but it didn't work. It was like two different games before and after their goal.
"It was a very stop-and-start game and there was no rhythm in the second half."