Second-half goals from James Milner and Brajan Gruda secured Albion their first Premier League win of the season, while condemning City - who scored through Erling Haaland -to a second straight loss.
Ex-City stopper Hart outlined how Tottenham pounced upon his old team's high defensive line in their 2-0 win at the Etihad last month, as well as highlighting how Fabian Hurzeler's side punished them.
The 38-year-old observed that substitute Rico Lewis, who is not a right-back by trade but has often played there for City, was caught out of position as Albion broke for Gruda's winner.
He said on Match of the Day, "I think defensively there are some alarming patterns already in the first couple of games.
"[Rayan] Ait-Nouri is very much a defender but he is attack-minded. [There is] no problem losing possession there (in Albion's final third), City are fully used to that. Four v four, they are very comfortable with it.
"But what will alarm them is how easily Brighton slice through them. John Stones is looking to play that high line again. [Kaoru] Mitoma is not offside, simple pass. James Trafford makes a really decent save.
"What is alarming again for City is how easily Brighton bypass that midfield three - they are not even in the running. Brighton look so fresh, one pass, Trafford is in a good position, makes a good save for his team.
"This is the real problem. This is the match-winning moment, this is Rico Lewis. He plays a lot at right-back, but he is not a right-back by nature, and he proves it in this instance.
"He has a look at Mitoma, who is in a dangerous position. Lewis seems Mitoma but he still chooses (left-back) [Maxim] De Cuyper and his pass. Rico has carried on, and Pep Guardiola has seen the problem. Hurzeler can't believe his luck; he's really excited.
"John Stones has had to make a 30-yard run to cover his team-mate, he's out of control, he's having to make some sort of contact for his team. [Yasin] Ayari turns it over, and in the blink of an eye, we have a four v two situation."
Hart stressed that this is not a "crisis" for City but they need to get on top of this quickly, especially as many fans were optimistic about their chances heading into the season and after thrashing Wolves 4-0.
Incidentally, before Lewis replaced Matheus Nunes at right-back, the Portuguese midfielder gave away a penalty for handling Lewis Dunk's shot - so their issues in that position may not be easily remedied.
"This is not a crisis, but it's a difficult moment for them," he added. "There was a feel-good factor going into the season, but this has put a puncture in their balloon. They are going to have to address those situations and look at themselves defensively."