Yes, a Battle Master can give up their single-attack Attack action to use Commander's Strike.

You appear to be confusing the Attack action with an attack.

The Attack action is one of the things you can choose to do with your action; others include the Dash action, the Cast a Spell action, and the Use an Object action.

An attack is anything you do that causes you to roll a die to overcome someone's AC. Trying to hit with a weapon is an attack, but so is using a spell that rolls against AC, such as eldritch blast. You can make attacks without taking the Attack action, e.g. attacking with a spell using the Cast a Spell action, attacking with a magic item using its own unique action, or attack with a weapon using a reaction (e.g. using the Ready action, or making an opportunity attack) or bonus action (e.g. from Two-Weapon Fighting).

The prerequisites for the Battle Master fighter's Commander's Strike maneuver are that you:

• take the Attack action, which always allows at least one attack, and
• forego one of those attacks, even if it is the only one

The rules for grappling and shoving a creature are similar.

No. You cannot forgo attacks you can't take

You can take only 1 attack

Say your character can normally make 2 attacks by using the extra attack feature:

Beginning at 5th level, you can attack twice, instead of once, whenever you take the Attack action on your turn.

The net's description says:

When you use an action, bonus action, or reaction to attack with a net, you can make only one attack regardless of the number of attacks you can normally make.

When you attack with a net you now can take only one attack regardless of your extra attack feature.

Thus you "have" only one attack now. It is worth noting that "number of attacks you have" is not something the game ever says. The only thing that is defined is the number of attacks you can take. And that number is now 1.

You are willingly foregoing those extra attacks as a cost of using the net.

You cannot forgo attacks you can't take

When you take the Attack action on your turn, you can forgo one of your attacks and use a bonus action to direct one of your companions to strike. 

Notice the word "forgo" which means "omit or decline to take". You cannot "decline to take" something that you could not have taken anyways. Like you cannot decline an invitation that was not given to you in the first place.

Since you've already used the net, you have no available attacks left to you. Thus, you have no attacks you can forgo.

Seeing as the Commander's Strike feature needs you to give up an attack and you have no more attacks to give up after using the net, then you cannot use commander's strike after using a net.

A heavy crossbow would work

Let me try to make this a bit clearer or more convincing using an example that does work.

Heavy crossbows have the loading property which says:

Because of the time required to load this weapon, you can fire only one piece of ammunition from it when you use an action, bonus action, or reaction to fire it, regardless of the number of attacks you can normally make.

This is very similar to the wording of nets with the major difference being that the loading property says "you can fire only one piece of ammunition". This means that you could easily drop the weapon and continue attacking with another one given the appropriate number of additional attacks. And thus one could also use commander's strike because you still have not spent those potential attacks.

But a net will not

However, the net does not make this statement instead just saying "you can make only one Attack". The easiest way to read this in light of the above is that the net takes so long and is so unwieldy to use that you have to use your entire attack action to wield it.

tl;dr

By using a net you are spending any additional attacks you have to attack with a net. You've essentially spent them and you cannot spend then again. The idea of Commander's Strike is that is that you give extra attacks that you could have made to someone else. But in this case you could not even make those attacks and thus do not have those attacks to give.