The Foxes netted an 89th minute winner from the penalty spot after Nathan Ake brought down former City striker Kelechi Iheanacho, who stepped up and fired beyond the sprawling Steffen.
The American goalkeeper was City's standout performer at Wembley, making some smart saves throughout the encounter, especially seconds before the interval as he spectacularly deflected Jamie Vardy's goal-bound effort onto the post.
The 26-year-old believes that the team will learn from the loss and bounce back stronger.
"The guys played really well and fought really hard," he said. "We just got unlucky at the end. Congratulations to Leicester. They played really well and tough today. It's an unlucky night for us.
"It happened really quick. We will learn from it. You always have to be ready for anything in these matches. You never know which way it is going to go.
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"I feel good right now. I feel healthy. The team has been playing well and training well. So I need to do my job when I'm called upon. We want to win everything and we want to lift every trophy. Losing is not fun. Coming second is not fun. We can learn from it."
Pep Guardiola's men begin the defence of their Premier League crown next Sunday in London against Tottenham Hotspur.
Steffen also spoke about that upcoming fixture. Watch the entire interview with the 'keeper via the video above.