The defender, 19, helped Birmingham knock out holders Arsenal in the quarter-finals before a semi-final win over Chelsea Ladies on penalties.
Manchester City are bidding to add the FA Cup to their 2016 WSL and Continental Cup (League Cup) titles.
"We don't fear anyone, especially not City," Carter told BBC WM.
"We have played them a number of times, we know what they are capable of and what they can do.
"We know we are good enough to compete with the supposedly better teams in the league, it's now about showing everyone else."
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Birmingham have drawn their past two league meetings with Manchester City, both of which were away from home, including 3 May's 1-1 draw in the Women's Super League One Spring Series.
The two sides were also level after 90 minutes in October's Continental Cup final, before England right-back Lucy Bronze won the game for Manchester City in extra-time.
"We don't fear them at all. Obviously they are a good team, they have a lot of great players," Carter said of the Women's Champions League semi-finalists.
"You show them a certain sort of respect, but you don't want to show them too much respect because they are just another player. It doesn't matter who they are."
Saturday's final at Wembley will see two close friends go head-to-head in Manchester City's defensive third, with centre-back Steph Houghton up against Birmingham striker Ellen White.
When asked about the threats Birmingham will pose, England captain Houghton highlighted her England team-mate White.
"My best mate Ellen," Houghton told BBC Two. "As a defender, she is one that you can't keep quiet. She is always trying to press the ball and she scores goals as well.
"I'm made up that she made the move to Birmingham. She is enjoying her football there."
White, 27, joined the West Midlands club from Notts County in January and netted the deciding penalty in 17 April's win over Chelsea in the last four.
The former Arsenal Ladies and Leeds Carnegie striker told BBC WM: "We have a lot of belief and ambition. We have beaten Arsenal and Chelsea. That has given us a lot confidence and momentum.
"We want to be competing and beating the likes of Manchester City, Arsenal and Chelsea and these top teams. This is the great stage to show what we are about."
At the other end of the field, Carter and the Birmingham defence will look to cope with World Player of the Year Carli Lloyd.
The United States forward, who has scored 96 goals in 235 international appearances, has netted twice in Manchester City's Champions League campaign, having signed on a short-term deal in February.
"Apart from ability, she brings her experience and leadership," Houghton added.
"No matter if you are a 17-year-old or someone like myself, who is more experienced, you are still learning from her and how she applies herself.
"She is always giving 100%, always wanting to do extra, always wanting to win. She has definitely brought a lot out of the other players and brought a lot to our side."
Birmingham City will not fear league champions Manchester City in Saturday's Women's FA Cup final, says Women's PFA Young Player of the Year Jess Carter.