Multiple things wrong in this post. To start, it's not on the manager that the majority of our budget was spent on two players, the manager isn't responsible for negotiating prices, he gives multiple targets and it's the people involved in transfers who negotiate prices. Not to add, both Lukaku and Pogba play in positions that cost an arm and a leg to buy top quality players in, something Pep didn't need to do. He already had KDB and Aguero, both amongst the best in their position in the league before he came in. To compare, Jose had Herrera, Fellaini (considered a joke on here), Carrick (way too old to be relied on consistently now), Morgan (lol), Schweinsteiger (see Carrick) and Wayne Rooney as his only established striker, not even comparable in the slightest. One had to spend big in those areas, one chose to, because the best striker in the Prem over the past half a decade didn't suit his needs. Going into the season with your only striker being an 18 year old, a 21 year old who just had his best ever season not even playing as a striker and Wayne Rooney who was just absolutely woeful isn't a risk any top manager would take. Pep brought in GBJ but he had Aguero to fall back on.
We might not have been the better team if Pogba played, but City were by no means dominating. They looked average and lacked penetration, their only two goals coming from terrible mistakes by Lukaku (who on another day remembers how to clear a ball and we draw or even win the game). Pogba would have resulted in us also creating more, it's hardly a coincidence that we score more goals and look more threatening when he plays. He's our only creative midfielder. If you were to take KDB and Silva out of City's lineup and play Fernandinho and another holding midfielder (No, Gundogan isn't a holding midfielder, he's also a creative one) you'd also see their football struggle as a result. Funnily enough, against us they had no penetration from the wings, both Sterling and Sane for the most part were kept quiet, instead most of their penetration coming from runs from deep by their creative midfielders mainly KDB. You can't expect to play two holding midfielders and not see your football get affected as a result. When we have no creative midfielder to play the ball out of midfield and to link the midfield/defence to the attack, you have no player capable of dealing with the press, no player capable of moving the ball out of the half, as a result the play gets restricted, you get boxed into your own half (as neither Matic or Herrera are competent at running with the ball) and thus your attackers have to drop back as a result - which is when our players begin to panic when getting pressed in their half. Pogba's absence severely hinders our play, not because he's an incredible player (he is) but mainly because he's the only creative midfielder we have. Him purely being on the pitch garners the attention of other players, allowing more space for other players to operate in. Not to add his ability to overcome the press with skill, his ability to play the ball into the channels etc along with everything else I mentioned. So yes, we might not have dominated against City with Pogba, but we would have been a hell of a lot more of a threat. Games at the top end are more often than not decided in the midfield and when you have no midfielder capable of dealing with a press, none capable of running with the ball or offering a proper goal threat, you're always going to lose that battle and when you lose that battle you get boxed in.
They didn't even need Aguero, most could argue he isn't even their first choice striker. We had Martial, Rashford and Lukaku and didn't scratch them, yet Sterling, Sane and GBJ didn't really offer much of a threat either - despite them being some almighty attacking force and having both their best midfielders available (something we didn't). As I said before, their penetration was mostly from deep.