A goalless draw did just that, they are now five points ahead of Forest with five to play, but means they trail top-of-the-table Scunthorpe by six points.
"We were aware that Forest were losing in the second-half and it meant we didn't go gung-ho for the win," he admitted.
"As it turned out a point was a very good result for us."
Johnson was ordered to the stands in the closing stages of the match after going onto the pitch to kick the ball away from Swans defender Izzy Iriekpen after City had been awarded a free-kick.
Although United fans may be hoping it is a sign of pressure getting to the Robins, Johnson was quick to laugh the incident off.
"I didn't think it was a red card tackle. I won the ball fair and square," joked League One's manager-of-the-month for March.
"I can only apologise and take whatever punishment comes my way.
"Managers shouldn't go on to the pitch, but there was nothing malicious about what I did. I just wanted to get on with the game."