However, the Blues responded with a crucial win against Manchester United at Goodison Park, thanks to Anthony Gordon's deflected effort, before Sean Dyche's side lost out against bottom-of-the-table Norwich City at Carrow Road.
"We're all hurting inside and it's very frustrating," said Brownhill. "We definitely have to be better, especially against teams around us.
"There's still eight games left and we've won games that have been written off. We've been here before. We're a fighting team but we've not managed to be on the right side of the result.
"The lads are always gutted after a defeat but we'll get together and put on another good performance next week."Burnley tackle Europa League hopefuls West Ham United on Easter Sunday, three days prior to Everton's next game at home to Leicester City.
After Canaries duo Pierre Lees-Melou and Teemu Pukki downed the visitors in Norfolk, ex-Bristol City man Brownhill said: "It was very frustrating. We went there to win and we didn't do that.
"I don't think the performance was too bad but it ultimately cost us. There are still winnable games but we need to get that consistency and momentum. There's a chance next week to put it right.
"There are still games to be won but we have to sort ourselves out. We’re going to go out to win every game. The games that we’ve got left, we’ve beaten the majority of those sides before, so I don’t see why we can’t go and do it again."
Remaining fixtures — April 17th: West Ham United (a); April 21st: Southampton (h); April 24th: Wolverhampton Wanderers (h); April 30th: Watford (a).
May 7th: Aston Villa (h); May 15th: Tottenham Hotspur (a); May 19th: Aston Villa (a); May 22nd: Newcastle United (h).