Nico O'Reilly scored early on for City and a strong defensive showing looked as though that single goal would be enough for the three points.
But a late header from Ulrick Ella consigned the EDS to a draw in a frustrating finale for Brian Barry-Murphy's side.
City did not have to wait long for the opener, as Oscar Bobb worked space on the left-hand side to cross for Kayky.
The Brazilian's header was saved but he was able to square to O'Reilly, who scored from close range to give us an early lead.
We continued to dictate the proceedings with Bobb, in particular, causing the Seagulls problems down the left-hand side.
And the Norweigan could have doubled our lead when a nice exchange with James McAtee played him through, but he couldn't find the bottom corner and the Brighton keeper saved his effort.
Moving into the second half, Barry-Murphy's side kept pushing forward to find a second goal.
Second-half substitute Iker Pozo was played through but shot straight at Brighton stopper McGill, before he created a chance for McAtee, but the midfielder fired over.
It was shaping up to be a great defensive display from the Young Citizens, but just as we entered stoppage time, we failed to clear away the ball and Brighton's Ella was at the back post to head home a late equaliser.
HOW WE LINED UP
And there was a City PL2 debut for Kayky, who started on the right with Bobb on the opposite flank, with O'Reilly up top.
WHAT IT MEANS
Our draw, combined with Arsenal's win over Leeds, sees us fall to second in the Premier League 2 table.
However, we are only one point behind the Gunners and two points ahead of West Ham, although they do have a game in hand.
The Elite Development Squad are also on the road next week, as we travel to Merseyside to face Everton.
Kick-off is at 13:00 (UK) on Saturday 6 November.
News about Brighton v Man City"
EDS eager to bounce back at Brighton, says Bobb
Oscar Bobb says Friday’s PL 2 trip to Brighton offers City’s Elite Development Squad the perfect opportunity to bounce back from Tuesday’s disappointing Papa John’s Trophy loss at Rotherham. Read more
Brighton v Manchester City EDS: Full Match Replay
Watch the full 90 minutes of our Elite Development Squad's latest PL2 clash away to Brighton and Hove Albion on CITY+. Watch more
Highlights: Brighton 1-1 City EDS
City's Elite Development Squad shared the spoils in our latest PL2 assignment away at Brighton. Watch more