Jose Mourinho's team retained their five-point advantage in the title race after City's David Silva cancelled out Loic Remy's opener on the stroke of half-time at Stamford Bridge.
Chelsea needed extra time to see off Liverpool in Tuesday night's League Cup semi-final and defensive midfielder Matic - who shielded his defence superbly as City dominated play after half-time on Saturday - said his team-mates felt the effects of a gruelling week.
"Especially in the last 20 minutes of the game we felt a bit tired but I'm happy because everyone gave 100 per cent," he told Sky Sports.
"It was difficult to run with the City players because they were more fresh than us."
Serbia international Matic felt the draw was a fair result - one that leaves Chelsea in control of the title race with 15 games remaining this season.
"To be honest we expected three points from today but if you see all the game I think a draw is a good result for both teams," he added.
"We had some chances, they had some chances and it is the same now - five points' difference. We are happy because of that and I hope we will continue.
"We scored in the 41st minute and it was a good moment for us to go into half-time 1-0 but City showed that they are a strong team - they never give up and they scored in the final minute of the first half.
"They are good and use any chance you give them but I am happy with how we played. We gave our best after Liverpool, when we played 120 minutes. For us it is a good draw."
