With one game left to play, Wolves are eighth in the standings on 51 points, five below seventh-placed West Ham United. The seventh-placed team will play in the qualifiers in the continent's third tier competition, the Europa Conference League.
"We are frustrated with the result. It has been easy to score goals against us in the last months," Wolves manager Bruno Lage told BBC.
"It is easy to find spaces against our defence and it is hard for me to be in this moment."
Bottom-placed Norwich should have opened the scoring within the first quarter but striker Teemu Pukki missed the target from long range in the eighth minute.
The Finland international eventually gave the visitors a surprise lead shortly before the break after he sent a low shot into the right corner.
Portuguese midfielders Ruben Neves and Joao Moutinho missed chances to equalise before the halftime whistle. While Neves' attempt was comfortably saved by Norwich keeper Angus Gunn, Moutinho's strike flew over the bar.
The France under-21 international nodded in a rebound following a free kick from close range, bringing up his first goal of the season.
The hosts' winger Pedro Neto threatened Gunn's goal twice more. While his header flew inches above the bar, he was also denied by a great save from the Norwich keeper.
The draw extended Wolves' winless streak to six matches.
"It was a really good, workmanlike performance but I'm disappointed we haven't got all three (points) because we could have been more than a goal up at halftime," Norwich coach Dean Smith said.
"[The equaliser] was preventable because it wasn't a free kick. Unfortunately, we have decisions like that go against us week in, week out. We are disappointed by that. We wanted to stop the bleeding today.
"Second half, we were careless on the ball and didn't keep it as well as we did first half. We thoroughly merited the point."