Mark Robins' says his side did not do enough after the Sky Blues were beaten 2-1 at the New Lawn.
Lee Collins' second half strike, just five minutes after Marc McNulty levelled from the spot, was enough to give the home side all three points in a closesly fought game in SkyBet League Two.
"We gave them chances prior to the goals and then we gave them the goals," said Robins.
"Burge did well with their first to make the initial save. We were second best all over the pitch.
"We have not done enough today. They were always first to the ball.
"It was a poor poor afternoon and there are no excuses here. This side have now done the double over us. Whilst they have worked hard, we should not be losing games like this when we are going for a promotion, no disrespect to Forest Green."
The Sky Blues were forced into multiple substitutions as the game went on with five City players recieving treatment at some stage, notably Jack Grimmer and Tom Davies who were both substituted.
"Davies has fractured his collar bone so that is going to be a while. At one stage we had far too many limping around and they wanted it.
"Grimmer's issue is with his hamstring. We do not know how bad it is, but he did it over-stretching for a tackle.
"Chris Stokes has also over stretched, and his hamstring was already so tight, so whether there is a tear there, who knows?
"Stokes had to finish the game, which did not matter too much becuase they were just seeing the game out and did not leave their back line for the last ten minutes.
He added: "This is really dissapointing. We have to put this behind us quickly and move on.
"There has been a lot of plaudits being given to the players over the last couple of weeks. They need to just get on with it and work hard and overcome the issues we have away from home.
"There are no excuses. We know how difficult playing three games in a week is, but everyone has to do it. We have got to be ready for the challenge.
"There are sixteen games left and still a lot of football to play. It is just frustrating when we get ourselves into a really good position and make it so difficut for ourselves."