Birmingham head coach Aitor Karanka questioned his players' effort after their dismal home form continued with a 1-0 defeat to Luton.
Dan Potts scored the only goal to condemn Blues to an 11th home game without a win, less than 24 hours after chief executive Xuandong Ren said Karanka had the "100 per cent" backing of the board.
Defeat left Birmingham with one victory in their last 12 Sky Bet Championship outings – three points out of 36 – to lie second from bottom of the table, a point below the safety line.
Potts headed home in the 31st minute after Harry Cornick launched a long throw-in and goalkeeper Neil Etheridge made a superb instinctive save to block James Collins' close-range shot on the turn.
Luton had several chances but Blues had just one effort on target, a header from Gary Gardner which was easily saved by Simon Sluga.
"The effort concerns me because we knew Luton were good at long balls and second balls and when they won every second ball it means they had more effort than us," said Karanka.
"We showed the players the set-pieces and throw-ins (before the game), yet they scored the goal from one throw-in – every single corner they headed the ball.
"So that is why I talk about the effort."
Asked if he meant there was a lack of effort from his players, Karanka said: "I think so because when one team wants to win, wants to win every second ball and wants to win every header, they (Luton) did it and we didn't.
"That's because they wanted it more than us."
When asked if he thought the players were still playing for him, Karanka added: "I hope (they are). After the last game, Scott Hogan said something like it's about them (players), so I don't think in one week everything has changed."
Regarding the vote of confidence from Ren, Karanka said: "I know how much we trust each other. He knows I am trying to do my best."
Luton manager Nathan Jones believes the best team won.
"I felt it was deserved. You're never totally comfortable but I felt we restricted them to very little," he said. "It was a scrappy game that lacked a bit of quality but I felt any chances that were had were had by us.
"We were a little bit disappointed not to go in further ahead. We then had to do the basics and I thought we did them really well in the second half.
"It's vitally important you keep moving forward – we had a tough January with four away games on the spin.
"It's nice now to back up our performances with points because we've started the month well, unbeaten and taken four points.
"We had enough of the game to have won and we did."
Luton's tally of seven away goals is the joint lowest in the division, but Jones is not too concerned about that statistic.
"We'd like to score more away goals but we are very difficult to beat," he said. "We're a team establishing itself as a Championship side."
A first win in four games lifted Luton up to 14th, and Jones added: "It does give you a little bit of a buffer but we're not looking there (down) and it brings others a little bit closer."
