Neil Warnock called for more optimism among Leeds fans after his side won at home for the sixth straight league game.
Ross McCormack's second-half goal was enough to ensure a losing start for Bristol City's new manager Sean O'Driscoll after Leeds were booed off at half-time.
Warnock said: "For me, the glass should be half full, not half empty.
"We knew it would be hard work because they have a new manager and are fighting for their lives. We got a grip at half-time and were a lot more positive in the second half.
"Tom Lees and Lee Peltier were fabulous at the back for us. Unfortunately, you can't please everyone, even when you have won six in a row in the league at home."
Of match-winner McCormack he said: "I thought if anyone was going to score it was Ross.
"It was a cracking goal, he deserved it and he covered lots of ground. He was a fraction away from putting one in at the end of the first half and looked very sharp."