Karl Robinson described MK Dons' 1-0 defeat to Port Vale as "a real low point" of his time in charge of the club.
The long-serving manager was booed by a section of the MK Dons fans when he clapped them after the game but insists he is not bothered by those who want him sacked.
When Dean Lewington was adjudged to have handled in the area after the half-hour mark, Alex Jones' initial penalty was saved but he smashed in the rebound.
MK Dons striker Kieran Agard had forced a save and Lewington had struck the post when the game was level.
Substitutes Nicky Maynard and Brandon Thomas-Asante both had efforts saved by Port Vale goalkeeper Jak Alnwick late on and Ben Reeves hit the bar with a free-kick but they were unable to grab an equaliser.
Robinson said: "I'm sick and I'm frustrated for the fans and the players and if I'm being honest today is a real low point for me.
"The first goal was always going to be important today and we've given a silly one away - and I can't take the blame for individual errors.
"We feel pressure from the first game of the season so that never really changes, but our performances have been excellent.
"If you want me out then fine, it won't bother me - but that's the prerogative of the chairman.
"We're dominating games, we're having possession and chances and we're just not having any lady luck at the minute so that needs to change for us.
"I get the frustration of the people in the stands but I'm just as frustrated - we're judging people on a fraction of a game, but the players aren't making these errors on purpose because they're trying their best."
The victory ended Port Vale's winless run away from home that stretched back to April.
And manager Bruno Ribeiro, who was appointed in the summer, said: "It was a great performance from everybody, the desire and the attitude was immense throughout the game.
"I'm delighted. Everybody played their part, from the starters and substitutes to all of the backroom staff.
"We defended as a unit and when we had the time to play the ball we did that too, which is a really important aspect for us.
"This is a very difficult place to come because they're still a very good side, and I still think they'll be up there at the end of the season.
"Every game is a difficult game in this league, whether they're home or away it doesn't matter - today it was just important to get the result though and we need to build on it now.
"We've got a great group of boys here because everybody works for each other - we all helped each other today, on and off the ball."