Forest lost 3-2 at home to League Two side Macclesfield Town, currently second bottom of the entire Football League, on Tuesday night.
They have lifted the League Cup four times, but bowed out at the first round stage as Brian Horton's side claimed their first win of the season.
It was the side's fourth defeat on the bounce, with the only solace being an opening day win over Huddersfield.
Megson fumed: "I'm taking a lot of stick for what is going on here and I don't like it, but I'm determined to sort it out.
"There has to be an accountability because if we are going to stroll about like we did in the first-half, we are definitely going to struggle.
"But if we can play all the time like we did in the second, then we can start getting results."
Forest took the lead against the Silkmen, but the visitors had gone into a 2-1 lead by the break and added a third in the second half.
Megson was left fuming at the inadequate display from his side, who were left floundering until they were forced to chase the game.
He added: "What has made me most angry is that as soon as we go 2-1 down to a team from a lower division than us, we then play in the second-half like we should be playing all the time.
"If we play like we did in the first half, which is strolling about thinking the world owes us something, we're going to struggle all the time."