The Baggies' boss was left fuming after the game at the Emirates Stadium, labelling the decision to award the penalty as "ridiculous".
However, Clarke says that the squad will not be thinking about the penalty before the game at the Hawthorns, or getting revenge for the incident.
"What happened is gone and we can’t do anything about it," Clarke told reporters. "I don’t use revenge as motivation.
"Motivation should come from the fact we let ourselves down last week. The lesson I learnt was in the first half we defended too deep."
Last Saturday West Brom were beaten 3-1 by West Ham, where Youssouf Mulumbu was sent off for picking the ball up and kicking it at Gary O'Neil after being fouled by the midfielder, and will therefore miss the game against Arsenal.
Peter Odemwingie and Goran Popov have also picked up needless red cards this season, for kicking Fulham defender Sascha Reither and spitting at Tottenham full-back Kyle Walker, respectively, with Clarke admitting they must take action.
"We have had three red cards," Clarke added. "All three were avoidable, so it's something we must address."