In truth, so did the hosts, who did so through Jonathan Kodjia’s 20th-minute penalty miss in a first half in which City looked the more dangerous team.
But Kodjia came back to haunt his former club with the deadlock breaker nine minutes after the interval, before Conor Hourihane wrapped up the points with Villa’s second five minutes later.
City struck the woodwork at 0-0 through Bailey Wright and immediately after the opening goal through Callum O’Dowda, while Johnson’s men also had a strong penalty appeal turned down.
“The first goal was a good goal but they both felt a little bit unlucky from our point of view,” the head coach told Bristol City Player HD.
“It was a tight game but we made it that way. In the first half we definitely edged it – we hit the bar and then got a bit of luck with the penalty miss.
“We just had a wobbly ten minutes when we dropped a bit deep – that’s when we need that strength of character to stay tight, go man to man and deal with situations.
“There was an absolute stonewall handball when the defender throws himself at it with his arms raised and I thought there was another one in there as well, but we’re not getting those at the moment.
“It’s a fine line between success and failure, but that’s the way it seems to be going for us at the moment. We’ve got to make sure we take our chances with our finishing.
“Saturday becomes a must-win game. The players showed the effort and the fans showed the effort – now we go back to Ashton Gate and give everything we’ve got.”
Meanwhile, Tammy Abraham is to have a second scan on his injured thigh back at Chelsea tomorrow (Wednesday) to assess his fitness ahead of Saturday’s home game with Burton Albion at Ashton Gate (3pm).