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Luton boss Graeme Jones had no argument with the home supporters after he was booed off following the 2-1 loss against Birmingham.
Town's third successive league defeat ensured they remained bottom of the Sky Bet Championship, with Jones, who was only appointed in the summer, coming in for criticism as he left the pitch.
He said: "They've got every right as we're on a run of a number of defeats, absolutely every right. But I think if anybody was a football man you could see we were short today.
"And as I've said over and over again, we need our best players on the pitch and we need to get some new players in to have a chance of competing at this level.
"I don't blame the supporters. You get beat again, especially today at home, they're allowed to vent their frustration.
"At the minute, I'm not doing a good job, the players aren't doing a good job, you have to hold your hands up. But we're under enormous financial restrictions in terms of attracting people to the football club and that's the truth.
"I never think about that (losing my job), all I think about is the solution. I had a question the other day about why do you change the team so much? Because I'm trying to find a solution.
"I know what the problems are because I work hard to try and find solutions and today, me, the players have failed."
Town trailed after just four minutes, with Blues striker Lukas Jutkiewicz heading home Jeremie Bela's left wing cross.
The hosts showed very little in terms of attacks until George Moncur came off the bench early in the second half, hitting the wall from a free-kick.
Luton were level after 62 minutes, though, when Harlee Dean fouled Matty Pearson inside the area, with James Collins rolling home the penalty.
But Gary Gardner restored City's lead just seven minutes later before Dean was dismissed in the closing stages for his second yellow after fouling Collins.
Town centre-half Sonny Bradley was denied a stoppage-time equaliser by visiting keeper Lee Camp's legs, as Blues did enough to end their own run of six league games without a win.
Birmingham manager Pep Clotet said: "It's been a tough month for us because there were a few issues that happened to us.
"We were unfortunate to have injuries on two of our centre-backs leaving only Harlee Dean in that position for us, and through the whole month it's been difficult for us to get wins.
"But last week we get Jake Clarke-Salter back into the team from injury and it was an important game for us in the league, as we are already coming into the game from a win against Blackburn Rovers in the FA Cup on Saturday.
"The fact that we could come here today and get this win will accomplish two goals. The first goal is to put a very healthy safety net between us and the teams at the bottom, and the second
goal to get us back in the wins, as it now means two wins in a row.
"For the team that's very important and now we have our eyes set upon getting back a full, fit squad next week, compete again and put our eyes up the table."
