The Tigers also blew the chance to register a fourth successive victory which would have moved them into the play-offs.
Brown said: "It was not frustrating as it was our third clean sheet in four games.
"But we didn't show enough energy to defend or even play in the first half.
"It was important we got to the end of the first half with a clean sheet and to have an extra man was a massive bonus.
"It was frustrating, though, in terms of our quality in front of goal.
"We didn't work the opposition goalkeeper enough but the effort was there for everybody to see.
"We're all disappointed but there's no divine right to win a game of football, 10 against 11.
"We couldn't do any more apart from that bit of quality in the final third."
Like Johnson, Brown was also hardly bowled over by the performance of referee Andy Penn.
"The referee made a rod for his own back because he denied us four penalty shouts and consequently he couldn't give Bristol City one at the end," added Brown.
"But the important thing is that we didn't lose and that we kept the run going."