The defender bemoaned the individual errors costing the Edinburgh club, who are reeling from last Tuesday’s Scottish Cup humiliation at Brora Rangers and Saturday’s home defeat by Queen of the South.
A small number of supporters protested outside Tynecastle Park prior to the weekend’s 3-2 reverse as calls for Neilson’s removal intensified. There have also been demands for Ann Budge, the Hearts owner, to step aside.
Hearts remain 13 points clear at the top of the Championship table but the last two results were unacceptable for many fans after some previously tame displays. Halkett declared that the squad still fully support Neilson and his coaching staff, Lee McCulloch and Gordon Forrest.
“Everyone is behind the manager and the coaching staff, 100 per cent,” said Halkett. “We come into training every day and we all enjoy it. We like the way the manager wants to play. In games like Saturday, individual errors are putting us on the back foot and costing us.
“I don’t think that’s anything to do with what the manager is doing or how he is putting us out. When you lose a goal like that in the second minute, the gameplan is out of the window.
“We are all behind the manager and it’s just about us as individual players going out and doing better.”
Mistakes again proved costly against Queen of the South. Connor Shields opened the scoring following Mihai Popescu’s slack pass out of defence and the striker’s exquisite lofted finish put Queens 2-0 up on 22 minutes.
Popescu headed Hearts back into the match before the interval and Armand Gnanduillet struck the equaliser on 72 minutes. However, a late own goal by Andy Irving handed the visitors their first win at Tynecastle for 58 years.
“From the start of the season we were heavy favourites to win the league,” said Halkett. “When teams play against you they lift their game that wee bit more because they know we are the biggest club in the league.
“For teams to take points off us is a massive achievement for them. At the moment, it’s far too easy for teams to do that. It’s something we need to rectify. It’s not good enough.
“Everyone is fully concentrated on making sure we get a positive result at the weekend and get this league over the line.”
Fans’ exasperation has increased sharply after the last two results. “They have every right to be angry and annoyed,” conceded Halkett.
“From a personal point of view I feel embarrassed and I think we owe them an apology because the last two games haven’t been anywhere near good enough.
“We spoke at the end on Saturday about what it means to play for Heart of Midlothian. Plus all the fans, it’s the club they love and I think they deserve better. It’s down to us to work hard and rectify it.
“Tuesday night was the one of the sorest moments and I think it always will be. For the next five games, we’ve got to go and try to win every single one convincingly to try and restore a tiny wee bit of respect from the fans – then look forward to next season.”