A prolonged calorie deficit over time will leave you feeling lethargic and tired, especially if you couple that with cardio.
There are a few ways to prevent the lethargy though:
1. Don't diet at too extreme a caloric deficit
The lowest you can safely diet at as a female is 1,200 calories/day. If doing this leaves you feeling weak and tired though, don't go lower than 500 calories below your maintenance.
What is your maintenance?
Your body requires a certain amount of calories to maintain it's current
weight (body weight in lbs x 15)...so if you were 150 pounds, that would be
150x15 = 2,250 calories/day.
To lose 1 pound you need to be in a deficit of 3,500 calories. So if
you ate 500 calories less than this 2,250 each day (1,750 cals/day) you would
lose 1 pound each week.
2. Drink coffee
Perhaps not as healthy an option, if you drink coffee when you're feeling weak/lethargic, it will give you some pep to keep you alert and energetic for a while after....
3. Add re-feeds to your diet
A re-feed is where you take 1 day in your diet to eat at or slightly above your maintenance caloric intake. This will re-fill your muscle glycogen and leave you feeling like you have energy again to handle the next few days of dieting.
You can find more info about how to set things up properly here.
