The Baggies have rediscovered their best form in recent weeks to record back-to-back victories over Liverpool and Sunderland.
Albion are seventh in the Premier League table, but Clarke thinks that climbing to fifth and earning European qualification is just beyond the reach of his current squad.
He told reporters: "I think we are still a little bit away from there.
"It is difficult to gauge the Europa League because it only goes down to fifth position at the moment. That's all you can say and maybe fifth position is just a little bit beyond us at the moment.
"I'm pleased we reached 40 points but also disappointed it has taken us to the end of February to reach it because we put ourselves in a great position."
West Brom go in search of a third successive win on Saturday against Clarke's former club Chelsea at Stamford Bridge.