The Toffees took the lead just after the half-hour mark through Marouane Fellaini but had to settle for a point as Carlos Tevez slotted home form the penalty spot just before the break.
Everton have a great record against City in the Premier League with eight wins form ten outings prior to the weekend, however, Baines said it was good to get away with a draw after the champions increased their output in the second half.
"It is a decent point,” said the left-back.
"We were under quite a bit of pressure in the second half and that point in the game I think we would have been happy with a point.
"We were still trying to hit City on the break but they played well in the second half.
"I think we defended well and this is a much better point than some of the other points we have picked up in recent weeks. This is the best of the bunch.
"When you come away to a team like this you expect a tough game.
"In the second half we showed that grit we need to come away from sides like this with a point."