Sweet said the performance at Lincoln had left him “very uncomfortable” and “emotional” as it did not reflect the way the team wants to play or the way the club wants to represent the town.
However, he said the summer transfer window had been the busiest in his 18 years as CEO and the club had “to allow ourselves a bad performance”.
Sweet continued: “We do need time for those players to settle. Occasionally we need to forgive a bad day. I am really happy with the way Matt and the players have responded from Saturday’s game. They get it.”
He admitted that speaking about the manager’s position publicly was putting extra pressure on Bloomfield and the squad heading into Saturday’s home game against Doncaster Rovers.
But he warned: “It doesn’t matter who is in the position – if we keep losing games, if we keep turning in poor performances, of course we’re going to part company with the manager.
“That happens at every single football club, including this one in the past.”
Sweet said there was an “edginess” in the atmosphere at Kenilworth Road at present, which was affecting the players, especially the younger ones.
“We’re not going to get promoted unless Kenilworth Road is a fortress – we’ve only ever got promoted when Kenilworth Road was a fortress, so somehow we need to turn that around,” he said.
“Success for us as an absolute minimum is play-offs but our desire is to get automatic promotion – and that’s our target.”
Sweet said the board had considered the possibility of bringing in a director of football but did not think it was the right way to go at the current time.
He added: “A director of football is a continental structure that supports a head coach rather than a manager.
“We want Matt to be a manager and manage that whole environment including medical, including sports science and getting heavily involved in recruitment, which he does.”