Hosts West Brom fell behind to Gary Hooper's 13th-minute opener before Clarke sent on Saido Berahino and Shane Long at half-time in an attempt to get back into the match.
Clarke's side did have the better of the second period, dominating possession, but were guilty of spurning their chances, with Stephane Sessegnon particularly culpable with one glaring miss shortly after the break.
The Benin international broke through the heart of the Norwich defence, but sent his effort wide of the post from 15 yards with just John Ruddy to beat.
That miss was to cost the hosts dearly as Leroy Fer wrapped up the win with a goal on the break a minute from time.
Defeat left Clarke in downcast mood after a frustrating afternoon.
"We created a lot of chances, but we didn't get the goal," said the West Brom head coach.
"We made it difficult conceding the first goal and from there it gives them something to hold onto.
"It was two teams feeling each other out and from nowhere they got the first goal and it set us on back and put us on the back foot."
Clarke was quick to defend Sessegnon, who also had a goal-bound effort seemingly blocked by the arm of Martin Olsson five minutes before his miss.
"We will keep faith in him," said Clarke.
"We will keep believing in him because that's the type of player he is, he got in a couple of great positions and contributed a lot to the team performance.
"Instead of rolling it six inches outside the post he should have rolled it six inches inside the post but these things happen."
It completed a bad seven days for West Brom, who lost 2-1 at Newcastle United last weekend before a midweek home defeat to Manchester City.
"It has been a difficult week," said Clarke.
"Three defeats are sore, painful and hard to take. Next week we have to go to Cardiff and be resilient and we have to start getting points on the board, there's no easy solution."
