It sounds like your being pegged back in your own half, so your defense is naturally dropping deep because of the constant pressure of you losing the ball and them attacking. As a result, they'll have a high back line which will make their defenders tight on your attackers, while your defenders are giving his attackers more space as he's camped in your half, and your defenders are sitting deep.
It sounds like you need to know how to play yourself out of trouble and attack better. That might sound counter intuitive, but I think its your use of the ball and attacking you need to get better at rather than your defending - well, for the moment anyway. You need to force him back into his half to get more room yourself. Your constantly losing the ball while under pressure and that's how your problems are happening.
Try creating a custom tactic with 'Player support' at 20 and 'Support range' at 0. This will bring your players closer to you so you can pass yourself quicker and more accurately out of trouble.(This is optional, but for the moment it might allow you to learn and understand how to play yourself better out of trouble.)
You also need to try to exploit a weakness of his constant attacking. That is, his high defensive line. Create one two's to get your players making runs to allow for through balls in behind his defense. Put players on manual runs also. Try not to put centre backs on runs as this will leave you exposed at the back if you lose the ball. Making runs will also cause players of his to be pulled out of position, which can be used as a decoy to create space elsewhere.
When passing balls to attackers who're tightly marked, try to quickly create a one two with them to get behind the defense, or protect the ball with your back to the defender until a teammate of yours becomes available to pass to. Don't try too much to beat the defender straight away with your attacker - one way you can though, is to hold sprint and press the stick diagonally to the side of the defender to beat him with a burst of speed. Not guaranteed especially if your tightly marked.
By attacking better, you'll peg him back into his half. You'll have a higher defensive line with his attackers having less space and your attackers having more in his half.
Edit: Try to not panic when your trying to counter attack out of your defense when under pressure on the ball. Don't just pass the ball out of hope some player of yours gets it, 9 times out of 10 you'll lose possession and be in trouble again. Hold it up if you have to until someone is free, or check your radar to see if someone is free across the pitch.