What do I do as black in this opening

Opening theory and the openings explorer on this website recommend playing Nf6 immediately on move 2. For example, 1. e4 e5 2. Nc3 Nf6 3. f4 d5 4. fxe5 Nxe4.

3...Bc5 was not a mistake. It's perfectly playable. The most commonly played move for Black after 4.Qg4 is 4...g6 (not 4...Qf6?!). Better White players will then reposition the Queen to attack f7 with 5.Qf3, but after 5...Nf6 6.Nge2 d6 there is plenty more chess to play.

3...Bc5 was not a mistake. It's perfectly playable. The most commonly played move for Black after 4.Qg4 is 4...g6 (not 4...Qf6?!). Better White players will then reposition the Queen to attack f7 with 5.Qf3, but after 5...Nf6 6.Nge2 d6 there is plenty more chess to play.
[game] ..
Wow love the game!

3...Bc5 was not a mistake. It's perfectly playable. The most commonly played move for Black after 4.Qg4 is 4...g6 (not 4...Qf6?!). Better White players will then reposition the Queen to attack f7 with 5.Qf3, but after 5...Nf6 6.Nge2 d6 there is plenty more chess to play.
That game is nice!

3...Bc5 isn't exactly a mistake, it is playable for sure, but 3...Nf6 is better, at least at the beginner and intermediate level. In the same way, you can play 2...Nf6 and at high level you'll be fine, but at lower levels playing directly into the Vienna Gambit doesn't usually go well.

I agree with you @Tarkil42. Nf6 is much easier for black than the sharper Bc5 for players who aren't familiar with the theory.

According to my database, based on 2,565 games total, Black wins 30.6% of the time with 3...Nf6 and 28.7% of the time with 3...Bc5. I find that difference statistically insignificant. I say play whatever makes you more comfortable. 3...Bc5 is played less often, so White is likelier less booked up on that move. 3...Bc5 would be my choice. I'm in good company considering the 2686 player agreed with me.