Heh this happens when our adult league team faces the best adult league team in the league. I know how you feel, it seems like no matter how hard your team tries, you guys just can't get the ball.
The problem is, they are using the full field its full advantage. They play every player, like tactically. Even though your team is trying to man mark or tackle, they just maintain possession. And after the game, your team is bushed and their team looks like they just got through their warm-up. Think of it this way, a game of monkey in the middle, and you guys are the monkeys. They're just moving around (not moving out of their position, but stretching the field), and receiving passes. They know their teammates well, they can pass and support, makes runs, etc., while your team is running around like a dummy. When we play, the main reason we lose is because we get impatient and start running after them, and when we move out of position, they exploit it and catch us sleeping. After a few more of these repetitions, we're already tired from all the chasing and they're just passing to each other like practice.
Just wait for them. Like them come to you. Defend deep, and don't be so eager to counterattack and play quickly. Make sure you make good use of possession, because they will and like they say, you can't score if you don't have the ball. The more players you have back, the harder it will be to penetrate, and you can intercept a pass, and hold it up for your team to regroup for an attack. Basically, as long as you know they're passing around, they won't do something extremely fast, so there's no rush. That's just my opinion and my experiences, if it's wrong then you can elaborate on what the other team does and we can decide from there.