The Baggies ended their three-match losing run, but the Scot was disappointed that they did not create more chances and ask more serious questions of their opponents.
Clarke's side's rapid start to the season has slowed in recent weeks but they remain in sixth place in the Premier League, level on points with Everton who sit above them courtesy of a superior goal difference.
"I can't say I'm disappointed not to win it because I felt the draw was the right result," the boss told reporters.
"We didn't do enough to get the three points, as the home team the onus was on us to go and get the win, which we tried to do, but it didn't happen.
"We wanted to put in a strong defensive performance to make sure the worst we got was a point and that's what it turned out we had to accept."
|WEST BROM TO WIN?
|8/1||West Brom are 8/1 to beat Norwich 2-0 with bet365|
Clarke admitted that West Brom's recent drop in form may have dented the confidence of his players in front of goal.
"When you come to a game on the back of three defeats there is always going to be that bit of nervousness about the players and spectators," he added.
"It's important we got a result to stop the rot. We got a clean sheet, which was important, and we recorded another point on the way towards the totals that we are hoping to achieve."