The first match in charge of the Canaries ended in defeat as they were knocked out of the FA Cup by a lower ranked team.
Jack Vale gave the visitors the lead at the start of the second half after a mix-up in theNorwich defence.
Pears denied the Canaries as they tried to get an equalizing goal.
Danel Sinani had a chance to win the game in the final moments, but his shot was blocked.
The fourth round of the FA Cup will be played between 27 and 30 January and the winner of that game will play the winner of the match between Forest Green Rovers and Birmingham City.
After Dean Smith was fired on December 27th, a rolling contract was put in place to find a replacement.
Tim Krul was one of six changes made by the 51-year-old.
After a backpass from the centre-back sold Krul short, the Canaries fell behind as Grant Hanley headed the ball into the net.
Bradley Dack squared for Vale to steer past a covering defender on the line after Dilan Markanday closed down the former Netherlands keeper.
Pears palmed away a low Gabriel Sara shot before Ben BreretonDiaz missed a good chance to make it 2-0 in the first half.
Six-time FA Cup winners Blackburn put in a solid defensive display after the break to progress to the fourth round for the first time in over a year, while Norwich suffered a third-round exit for the first time in four years.
The Canaries are three points off the play-off places in 11th after being demoted from the top flight.
The boss of Norwich told the radio station.
Football players don't get what they deserve.
This was quite good after only a few days of working together. I've seen some great stuff.
The players wanted to play from the back and were very brave. We have made mistakes before the goal.
I raised my hands for it to happen. It must not happen often. We didn't create enough clear cut chances.
Jon Dahl Tomasson is the manager of the football team.
It was a great victory.
There was a positive energy around the stadium when you came with a new manager.
All the players had good answers when they were asked many questions.
We played with passion and determination. The clean sheet was crucial.