Despite dominating and piling on late pressure, the hosts were left to rue missed chances, as we faced a spirited Seagulls side who proved impenetrable, with goalkeeper Megan Walsh in fine form.
City headed into the clash with a perfect record against Brighton, having won all five previous encounters, scoring 23 goals and conceding just once from the penalty spot.
However, manager Taylor had warned against complacency beforehand with Hope Powell’s side having kicked off the new campaign with an impressive triumph over Birmingham City.
As was the case last week in the victory over Aston Villa, City came flying out of the blocks – almost securing the perfect start as free-kick specialist Steph Houghton saw a low curling set-piece thwarted by Walsh, and Georgia Stanway dragged an effort wide.
The opening half hour proved a somewhat sloppy affair with neither side managing to gain a foothold in the game. Brighton were content to counter with their best chance a long-range Danni Bowman strike, which did little to trouble Ellie Roebuck.
City built a period of pressure as the half drew to a close, forcing the best of Walsh, who did well to deny Chloe Kelly and Stanway.
The latter almost caught the Seagulls' shot-stopper out as a cross-shot was almost fumbled over the line but the visiting 'keeper recovered to gather.
Mewis also had the chance to try her luck but opted to unselfishly square for Ellen White – only for the Brighton defence to scramble clear.
In the last major action of the half, Inessa Kaagman attempted an ambitious volley at the other end, which bounced harmlessly wide.
The second half proved an equally even contest with both sides in search of the opener.
Though not for the want of trying, a frustrating second 45 bore little in terms of sustained pressure – though both teams had opportunities to nick it.
White was unfortunate to see an effort roll wide, while Houghton could only find the side-netting, and Stanway and Kelly smashed off-target.
As City pressed in the dying embers, pushing for a late winner, the valiant Brighton could have snatched all three points themselves.
Maya La Tissier stung the palms of Roebuck, while Kayleigh Green and Bowman also went close, but time ran out for both sides.
What it means
City start the season with four points from our opening two games.
Arsenal and Everton lead the way in the FA Women's Super League with six points apiece - the Gunners top on goal difference, following their 9-1 win over West Ham on Sunday.
Four teams sit on four points: Chelsea, Manchester United, Brighton and City.
How we lined up
New recruits Bronze and Greenwood were thrown straight into the starting line-up, with the left-back making her debut and Bronze marking her homecoming.
The game arrived too soon for United States star Rose Lavelle, who joined up with the squad this week, following a fortnight of quarantine.
Roebuck kept her place in goal, shielded by a backline of Greenwood, Gemma Bonner, Houghton and Bronze.
City extend our unbeaten home record to 29 games (24 wins and five draws) in all competitions, and 23 home FA Women’s Super League games.
City return to action, following an international break, as the 2019/20 FA Women’s Cup resumes.
Taylor’s side travel to Leicester City in the quarter-finals with either Arsenal or Tottenham Hotspur awaiting in the last four.
Having lifted the trophy in 2019, City are the current holders and will look to retain the title as the first of two editions of the competition this season.