Sounds like you did pretty good! You make a good point about portion of turn remaining and ability to dig in. In some areas, the Germans will be hard pressed just to establish a defense, much less try going on the offensive. On the first turn, you probably won't have to worry too much.
As the game develops, you are going to get a good feel for where things are rough-going. You may see the Axis concentrating attacks on very specific areas. So in these areas, you always want to try to consolidate your positions as much as possible. If you keep one regiment per hex (3 bn), or 1-2 battalions plus divisional support assets...try to keep one dug in, use the others for offensives. Always have another unit ready to move into territory to dig in there, too - while continuing to press the offensive. One unit acts as your shield, the other as your sword.
What's your situation looking like in the Carentan area?