Nathan Dyer's first-half lob gave the visitors the lead after just 10 minutes after capitalising on Sebastien Bassong's mistake.
Gary Hooper's stunning volley deep into first-half injury-time gave the home side a share of the points, however, and Swansea were perhaps lucky to come away with a draw.
Laudrup's thoughts after the match reflected as such, as he pinpointed Dyer's serious injury - a suspected ankle fracture - on 40 minutes as the turning point.
Speaking to Sky Sports, Laudrup said: "On one hand, in the first half we controlled the game well.
"It's the difficult thing to score the first goal, but a fantastic equaliser and the injury just before half-time made it difficult.
"It was difficult for us to come into the dressing room, and in the second half they started better than us.
"They're very good at set-pieces, but I think the game drifted away. Suddenly, Norwich get one chance out of nothing, then we get one.
"The only thing you can do is look at things through a certain pair of glasses, and I'm looking at it through a positive pair."
With the draw, Swansea still sit in 10th place with 20 points as Laudrup hopes to improve on last season's tally at the halfway point.
He was also insistent that his squad are dealing with a hefty fixture schedule, with the Premier League, domestic cups and Europa League all being balanced by the Welsh side.
He added: "I look at the points. It's a draw, and we've reached 20 points already after 16 games.
"Last year we had 25 at the halfway stage, so let's see how far we can go.
"Today was the 27th game already I think, but everybody's playing and they feel a part of the squad. We just hope we can keep on going.
"We've played seven in the last 20 days, and all the travel problems with delays makes it difficult. It's what we wanted this season however. We're in Europe, and we're all happy.
"It's been a tough couple of weeks, and it could have been better this week. In the end, the bigger picture shows that we've got the points and we're into the last 32 in Europe."