Arsenal were controlling the game but, after Per Mertesacker was sent off and James Morrison scored the penalty that followed his tackle, the Baggies were handed a lifeline back into the match.
However, despite creating good chances late on through Romelu Lukaku, Shane Long and Gareth McAuley, amongst others, West Brom were unable to take advantage of their numerical superiority as Arsenal held on.
Clarke admitted that, without the penalty decision, his side would have struggled to get back into the game, but felt that the Baggies created more than enough opportunities to have expected at least a draw.
"Obviously with the penalty decision came the red card, and I don't think anyone could argue with that," Clarke said.
"From there, with 11 against 10 we had a right go. We created chances through good football and we created chances through just getting the ball into the box.
"Chances fell to people that you would normally expect to score. Perhaps today just wasn't our day."
West Brom remain in eighth position, but Clarke insists he will not allow the season to end tamely.
He said: "If you had asked me that after the West Ham game last week, I would have said yes.
"The response was good today. The performance today deserved to get something from the game. I don't think you can say we took it easy or didn't display a determination to get something from the game."