Shane Long's brace in the opening 11 minutes looked to have West Brom headed for victory at The Hawthorns on Monday.
But second-half goals from Karim El Ahmadi and Ashley Westwood saw Villa secure a point in the West Midlands derby.
Clarke felt his side should have held on for three points and rued not extending their lead in the second half.
"When you're leading comfortably 2-0 midway through the second half, you feel you should go on and get the three points," he told Sky Sports.
"But the energy of the substitutes seemed to unsettle us a bit.
"We gave away a bad goal, gave them a bit of momentum in the game and they took advantage of it. I think we missed one clear-cut chance to make it 3-0.
"I think if it goes 3-0 at that stage it's probably over, but in a local derby you never know.
"We knew that the next goal was going to be crucial."
Clarke praised striker Long, who set up his first on three minutes with a wonderful first touch and completed his brace with a chipped finish.
"Shane's been working hard for that type of performance," he said.
"He's in a good moment. Strikers are like that, they like when the ball's hitting the back of the net.
"You can see with the first goal - it's out of this world really. It's a great touch over his shoulder, good second touch and finished well with his left foot.
"His second came because he reads the game well. It's good for Shane. He's been in a good run of form for us and hopefully he can keep it going."
West Brom sit 11th in the English Premier League with 15 points after six draws in their opening 12 games.
Clarke wants his side to build on their draw with Villa when they travel to take on Newcastle on Saturday.
"I feel as though we're drawing too many games. We have to turn those draws into wins. There are some positives, especially from the first half when we controlled the game very well," he said.
"We'll look to build on that next week in the difficult away game at Newcastle."
