Town have given themselves a lot of work to do to finish in the top seven, having suffered back-to-back defeats against Boreham Wood and Dagenham and Redbridge, leaving their fate out of their own hands.
Halifax are now 10th and realistically need to win both their remaining games, starting with Maidenhead on Saturday, to give themselves a chance.
But Byrne says the squad still believe they can do it.
“100 per cent, we believe we can beat anyone, we believe we should be higher than what we are now,” he said.
“We should easily be in the top seven, everyone who is in there now we’ve beaten, so we don’t fear anyone.
“On our day we can beat anyone so we definitely believe we should be in the top seven.”
Byrne says Town need to put the disappointment on last Saturday’s 3-0 defeat at Dagenham out of their systems and focus on bouncing back at Maidenhead.
“It was a frustrating game,” said the defender. “Obviously one we needed to win, so to go out, not really play too well and concede three goals, it was a frustrating game.
“Other results didn’t really go our way. We’ve been in the play-offs pretty much the majority of the year so to slip out with two games to go, it’s a bit of a kick, but it’s not finished yet, there’s still a bit to go.
“There’s two games to go and if we win those two games we’ll be right back in it.
“In football, you need to not get too high with the highs or too low with the lows and just move onto the next game.
“We still have a chance, it’s not like we’re out of it completely, but it was obviously a frustrating one and we just have to move on as quickly as we can.
“We had a game-plan, and I thought it could have worked.
“They changed it after 20 minutes in midfield, they’re on a good run, they’re very confident.
“We missed a chance early on, we had other chances and it could have gone the other way.
“But at Maidenhead, we just need to be strong, we need to be defensively solid and get back to what we were doing, be confident, attacking teams, going forward.
“Obviously there’s the possibility of having Jamie (Allen) and Jake (Hyde) back, which will strengthen our team massively.
“Come the end of the season you need a bit of luck on your side as well.
“We need to get our game plan right, go there and attack them. There’s no pressure, don’t be scared of anyone, we just need to get the three points no matter how they come.”
Byrne, who has started more league games this campaign than any other outfield player for Town, says success for the team this season would be finishing in the top seven, but not as nearly men.
“I don’t see it as a good season or a good achievement if we don’t finish in the top seven,” he said.
“I’d imagine at the start of the season, a lot of teams didn’t think we’d be up there but we know as a club that, with the lads we have, the experience, the youth, how well we’ve played, how well we’ve done against teams, we don’t fear anyone. We’ve beaten all the top teams.
“For me, and I’d imagine the team, it would be a disappointment to not finish in the top seven. A failure really.
“As a team that’s what we strive towards, and we need to get there.
“We went on a great run where we were winning game after game.
“Against Stockport it was a very tough game, half a chance and they go and win it.
“You’re thinking ‘we need to go and beat Yeovil’ and we did and you think ‘right, we’ll kick on from here’ and it’s a step back.
“It’s one of those things after that many wins where you think ‘we’ll get over the line and once the play-offs come anything can happen’.
“So it’s frustrating to have these two games left when we should be secure, but we’re confident that we can go and beat anyone.
“It’s frustrating, one win, one loss, but that happens, it’s one of those things.”
Byrne said getting over the line is all that matters now, however the wins come about.
“It’s just having that composure and understanding that it’s just another game of football,” he said.
“The gaffer spoke to us about playing our way, and we want to play our way, we don’t go out in a game to just hoof it and not play the style of play that we want to put in on the pitch.
“But at the end of the day, we don’t really care how we get the three points, we just want the three points.
“It doesn’t make a difference how you get them.
“At Yeovil, we won 3-0 and everyone might have thought we were brilliant, but it’s just about getting the three points at this time of the season.”