We were much improved in the second half, dominated possession and a magnificent goal from Gareth Bale levelled the scores with 11 minutes remaining.
We were then a fingertip away from taking maximum points in the final minute as Canaries goalkeeper Mark Bunn turned aside Gylfi Sigurdsson's goal-bound drive from 20 yards.
Lewis Holtby also impressed in a 20-minute cameo and was involved in the early stages of Gareth's goal with Jermain Defoe.
"It was a difficult game," said Andre. "Norwich put in a really good first half performance and our second half performance was very good as well.
"At half-time the players recognised that they wanted to change their attitude and they really made the difference in the second half.
"It was an extremely good second half - the power, the ambition and playing attacking football in difficult circumstances.
"After we made it 1-1, we had chances to make it 2-1 and it's a pity that didn't happen.
"Hopefully the second half will be a good example of what we want to do at West Brom."
In tricky, windy conditions, Norwich started well and deserved a 1-0 half-time lead after Wes Hoolahan fired home in the 33rd minute.