In games like this, I believe we should be playing 3 in the middle. City played with Silva and KDB around and in front of Fernandinho and they had the numerical advantage (as well as better quality).
Playing with Mata-Herrera-Matic would have been better, with Pogba in Herrera's place normally. Lingard did not do badly in the derby and we've seen how deadly he can be on the counter, but he's not great at retaining possession and recycling the ball like Mata is.
Going forward, we either need to sign another capable midfielder or give Pereira a go. Pereira did really well in the friendlies as a playmaker I think he's worth a chance. Though signing another CM if Fellaini and Carrick are on the way out might also be required.