Brunt is keen to ensure Albion take their final few games seriously.
The Albion skipper said: "We didn't help ourselves on occasions at Upton Park but we move on and have to see how well we can push on.
"It was disappointing how the game went on Saturday. We started well, moved the ball around well but some of our play was schoolboyish. In the second half we created some half-chances but it didn't drop for us.
"We're well safe but that's not the point for us because we still have targets and want to finish the season well.
''We don't want the season to peter out.
"We need to bounce back against Arsenal."