The Baggies have reached the 40-point mark in the Barclays Premier League via back-to-back wins over Liverpool and Sunderland and are only two points adrift of sixth-placed Everton.
Clarke is now targeting 50 points but thinks the Europa League could just be out of reach, especially if only the team which finishes fifth is eligible at the end of the campaign.
He said: "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.
"I was hopeful we could reach the target a little bit earlier. The lads know me well.
"I don't smile, I'm a little bit grumpy and I just keep pushing them.
"I know the talent we have here and I know what we have in this group, and I want to keep pushing them so hopefully they go on and have a really good season.
"Fifty points now becomes the next target and a realistic one."
But when asked if the Europa League was a possibility, Clarke said: "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."
Striker Shane Long has given Clarke a boost by insisting he wants to remain at the Baggies next season.
Clarke could lose the services of on-loan Chelsea striker Romelu Lukaku and the wantaway Peter Odemwingie this summer, but Long is content to stay.
The Republic of Ireland international has been in fine form this season and the subject of speculation linking him with a possible move away from the Hawthorns.
Long said: "Am I committed to West Brom for next season? Yes, I'm happy here. I like playing for the manager here, he is very good, and I'm learning a lot every week.
"The lads are a good bunch, the family are happy up here, so I'm not looking to move on.
"I'm concentrating on this season and hopefully getting a few more goals before the summer and kicking on from there."
Premier League Without Top 6 12/13 Win Outright: West Brom 11/1
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