Notts had some chances early in the game and could have been a goal up but for Karl Hawley's shot which hit the post inside the first 25 minutes.
But City pounced when they had to, scoring through Patrick Vieira eight minutes before the break and then hammering home a further four goals in the second half.
Ince said it was his team's inability to find the target when they had chances which lost them the game.
"I thought we did ever so well and with a bit of luck we could have been 1-0 in front," said the former Manchester United midfielder.
"That is what you need when you come to places like this. We started well and at times it felt like a home game.
"We were ready for it but when you get your chances you need to take advantage and but for the width of a post it didn't happen because that would have set us off nicely.
"I'm disappointed for the players. We worked very hard over the last few days on stopping City and I thought we dealt with that very well but to lose two goals from set-pieces was disappointing, especially the timing of them.
"This is the wealthiest team in the world and we have matched them for an hour.
"In the last game we were 10 minutes from knocking them out so we have to take positives from that.
"A score of 5-0 doesn't justify how well we played as a team.
"You know you are going to get tired and we needed that goal while at 2-0 to keep us in the game."