Goals by Danny Handling and Rafa De Vita at Ainslie Park secured the Citizens a precious three points in their quest to reach the League Two promotion play-offs. Bobby Barr had equalised for the visitors.
However, defender Jordan Tapping limped out of the game after only three minutes of action with a hamstring injury and he now looks set for a spell on the sidelines alongside Alex Harris and both Blair and Liam Henderson.
City manager Naysmith said: “We’re trying to manage it as best as we can and make three of four changes in most games to freshen things up because the players are carrying knocks and playing a lot of minutes.
"We could have a couple back for the weekend against Queen’s Park but we’re a wee bit stretched. Every team is in the same position with so many games in such a short space of time.”
On the 90 minutes itself, after which Edinburgh City remain in second spot in the table, Naysmith added: "I think the goal was fitting to win any game but whether or not the performance was is another thing.
"I think (Brechin boss) Michael Paton will feel a wee bit aggrieved not to have taken a point.
“We got off to a dream start with getting the goal so early but I think that’s probably the worst thing that could have happened as maybe the players thought it was going to be an easy night.
"But Brechin produced a well-worked equaliser and we had Calum (goalkeeper Antell) to thank for getting us to the break level-pegging.
“We asked the players for a reaction in the second half and we certainly got that for the first 15 or 20 minutes.
"We were finding more space and getting more shots away. But if you don’t score when you’re on top you are always worried a wee mistake could cost you, but fortune was on our side as Rafa has hit a sensational strike to win us the game.”
Edinburgh City have won six and drawn one of seven league games under Gary Naysmith and he is League 2 manager of the month for March.