Sean Dyche’s men lie in seventh spot ahead of today’s visit of Liverpool – seven points clear of Leicester below them.
Their incredible first half to the season has encouraged hopes they can defy the odds and finish within the European qualification places.
Striker Barnes said: “We’ve got to believe that Europe is a possibility and that’s what we’re aiming for.
“We’re seven points clear, so why can’t we go and challenge the top boys?
“Every game is tough in this league but we’re there for a reason and that’s because we’ve done so well.
“It just shows how far we’ve come as a group of players but we want to keep striving for more and get as many points on the board as possible.
“The table and the points don’t lie. We are where we are on merit and we need to start believing more and keep striving towards being in the Europa League.”
Burnley were the better side against Huddersfield and might have won had referee Paul Tierney not ignored Jonas Lossl’s trip on Jeff Hendrick inside the penalty area in the second half.
Barnes added: “We get nothing, but it’s a hard one to take because Jeff won’t go down and dive.
“You can see on the video that he’s caught him. I don’t know how we didn’t get the penalty; that could have changed the game.”
Burnley’s last three meetings with Liverpool have seen both sides claim a victory apiece and draw at Anfield in September.
Mo Salah is a doubt after limping out of Saturday’s 2-1 home win over Leicester after his matchwinning brace took his season tally to 23.
Clarets boss Dyche said: “Salah is a fine player, but it isn’t just about him because the top teams in the division, the superpowers as I call them, they have threats all over the place.
“You can’t just look at one player. Harry Kane, what a player, what a professional, but Tottenham aint bad elsewhere.
“You look around that team and think if he has a quiet day, they have enough to open things up – and Liverpool are the same.
“Man City too obviously and Arsenal still have question marks about them, but they look decent to me.”
Huddersfield will head to Leicester on the back of a four-match unbeaten run which has left them well placed to beat the drop.
Defender Scott Malone said: “We’re going there with massive confidence. We know we have to play a little bit better with the ball, but if we take that fighting spirit to Leicester, I’m sure we’ll get a good result.
“Staying in this league would be fantastic and it’s more than achievable. We’ve shown a lot during 2017 and I’m sure 2018 will be the same.”
With the transfer window now open, Terriers boss David Wagner said: “We will have our eye on the market and if we can and if it makes sense, then we will try to do something. If not, then I am happy with my squad.
“We have delivered so far, even if everybody knows that January and February are no less intensive.”