This is actually quite a sensible question and it isn't about the English word 'counter' as JiK suggests, but about the English word 'play'. ;-)
To have 'play' in a position basically means that you are able to create threats. The possibility to create threats isn't really linked to how complicated a position is. But a position in which only one player can ...
It looks like your position fell apart pretty early on, a symptom of poor opening theory. Your King and Queen were exposed to attack within the first few moves, and White ruthlessly exploited that opportunity.
The first move that Stockfish classifies as a blunder (yes, there's more than one) is 5. … h6?? where you attempt to directly attack the advancing ...
What's the main idea of this opening?
Main ideas for white:
surprise weapon as it is rarely played (since it is not all that good)
playing the Dutch opening with an extra tempo, but this is not a big deal IMO
avoiding opening theory as you can basically learn a "system" (certain position of pieces that you want to achieve) and follow this almost ...
Do not play 3...Nxe4 in response to 3. Nxe5.
I feel this important aspect is missing in the other answers. You can see the primary reason it doesn't work in your game - you end up losing the queen. Given that you can't just move the knight after 4. Qe2, your next-best option is to play 4...Qe7 5. Qxe4 d6 (or ...f6), which still results in you losing a pawn. ...
This part of the answer pertains to the first version of the post, where (due to a typo in setting up the diagram in OP) the move 4...f6 was played:
It started to go wrong for you from the move 4...f6, which just walks right into Qh5+ completely winning for white:
[title "why 4...f6 is a mistake"]
[fen "rnbqkb1r/pppp2pp/5p2/4N3/4n3/8/PPPPQPPP/RNB1KB1R w ...
In Damiano variant you respond 4. ... Qe7 to 4. Qe2. Yes, white takes the knight faster than you, but then you simply make d6 move, and if white knight retreats, white loses Queen. So to black's 5. ... d6 white have to respond with 6. d4, then: you take knight with the pawn and white makes a move dxe5. After those there's a bunch of possibilities that are ...
The two answers have already provided a very good explanations of the Bird's opening. So mine can be viewed as an addition.
is a known gambit and is reasonably sound. Followed by 2.fxe5 d6 3.exd6 Bxd6. Black sacrifices a pawn but gets ahead in development.
I like to point it out for two reasons.
1) It is one of the approaches to play against the ...
There is a saying that "the best way to refute a gambit is to accept it", attributed to Steinitz. While sayings in chess often have exceptions, I think it does apply to this particular case. If you go by either the Stockfish evaluation (-0.8) or the results of games between highly rated players (67% win for black out of 12 games), the gambit is a mistake.
What's the main idea of this opening?
This is basically white playing what is normally a black defence, the Dutch 1) d4 f5, with a move in hand so the idea is the same - white will develop his kingside quickly with the knight on f3 behind the pawn, castle kingside, maybe bring the queen over with Qd1 - e1 - h4 if there isn't already a pawn on g3 and then ...
I must quote some thoughts on bird opening from gufeld's book , "1 f4 d5
Avoiding the sharp play of the
From Gambit ( l . . .e5 ! ?), Black is
ready to play against the Dutch
Defence by the first player.
The attempt to prevent the fianchetto
of Black 's king' s bishop is
unsuccessful: 2 b3 Bg4 ! (hindering
the development of White's kingside)
3 Bb2 Nc6 ...
I could say something about a counter attack from a beginner's point of view:
What is a counterattack?
If one of your pieces is threatened by your opponent, then you should threaten the opponent's highest value pieces in your next immediate move (at least that piece should have higher value than your piece which is under threat).
If your rook ...
Counter play, especially when down material, is often about creating dynamic chances. So you should probably work in that area:
Study the games of some attacking geniuses like Tal, Shirov, Morphy, Anderssen.
Work through some good books on attacking chess.
Play some gambits in training games.
Train tactics, but thats a given anyway.