Don't understand all the negativity about the 2nd half.
Until the 60th minute we played an very good game and imho the lead was deserved - both sides had some chances, we have been excellent in transition, Spurs had some really creative moments with Son/Eriksen/Alli and Kane was phenomenal. Jones again not a chance against him. But we looked a bit better i think and had more clear chances.
The moment the whole dynamic of the game changed was around the 60th minute when Pogba lost the ball and they played a nice counter with Alli ending in front of de Gea who saved good. Until there we had a lot of chances because we played offensive but there the players/coach realised that it is too dangerous against that Spurs. Eriksen/Alli/Kane are all excellent in playing passes in counter attacks and Son, but also Alli/Kane are also really good in getting into the right positions and finishing these attacks off. So we became more defensive and Spurs more offensive. Just a normal thing in a game between two top sides - the leading team defends, the other one pushes for the equaliser. Even under Mourinho we looked like the better team in our 2nd half against Juve at home where we lost 1-0 as they tried to defend the result. Even City often sits down deep in this top games when they are leading.
The really important thing is that we didn't play this defensive at 0-0. It was an entertaining, good game between two offensive sides who wanted to win. When Spurs would have scored i am certain the dynamic would have changed and it would have been an open game again. But fortunately they didn't.
Only negative point:
In these 30 min i think we could have defended better at times. Don't think Young, Jones (especially) and Shaw will be good enough to play for us as first choice when we want to be successful again. And because of our bad defending Spurs would have deserved one point. But the plan for the game was good, it was not "Mourinho-like", as we would have sat back from the first min under Mourinho and here we did after 60.
E: As an good example, look at the last clasico. Barcelona was absolutely destroying Madrid, still Madrid had dominated the game completely for ~25 mins (45-70). Not only scored their goal, but also had chances over chances for the equaliser and even the lead. Still Barcelona deservedly won 5-1. That is football, you always have an opponent. Today we had an really good one, away from home. Who expected us to win comfortably doesn't have recognized that we are playing with an individual bad back four.