Yaya's laziness was solely responsible for that first goal, everything after that is a reaction by other players to try and mop up his mess.
Otamendi was absolutely right to step up and try to block/intercept the only option Kouyate had to pass to, he cannot think that Yaya having a 4/5 yard head start on Kouyate is going to get beaten one vs one. As a consequence of Yaya letting his man stroll past him, Otamendi has no alternative but to leave Valencia to try to get back at Kouyate. Delph can see Otamendi is stranded and has very little chance of getting back at Kouyate so busts a gut to try and block the shot/cross which he successfully does, an unfortunate bounce and the rest his history.
If you genuinely think we move the ball quicker when Yaya is on the pitch then god help you, if anything he's the main reason we're so lethargic in possession. **In regards to that statement I completely retract it if you're basing your statement as a comparison with Fernando**. As I see it we would be far quicker not only winning the ball back but also on the counter attack if we used Fernandinho and Delph, we would have far more movement from either of them running past the attacking midfielders and striker(s) to create more space for Silva and De Bruyne which would considerably speed up our attack and improve our movement against 'park the bus' tactics.