Intense training, particularly training that increases your strength (and consequently your muscles) not only burns a lot of calories, but your body requires more just to recover. When I train I use a heart rate monitor, and while it isn't perfect it does give me a good indication of the number of calories I burned during the training session. On average I burn about 1000-1200 Calories during the training session. If I cut out the assistance exercises and conditioning I'm still burning over 600 Calories. That's just the deficit I racked up during the training time. Assuming my BMR is 2400 Calories/day for the easy math, my body is only burning 100 Calories at rest. That's 500 more Calories on a light training day than I normally would burn.
Protein is an essential part of recovery, as it helps your muscles rebuild and make themselves bigger/stronger. However, it is also very thermogenic--which means it requires more energy to digest. Don't forget that your muscles still need energy. Energy can come from both fat and carbs. Mix it up.
So let's say your intense training session has you burning 1500 Calories and takes you 90 minutes. Let's also say you are burning 2400 Calories a day, partly because the math is easier, and partly because there isn't a big difference in hourly Calorie consumption with a slightly smaller number. In an hour and a half your body will have burned 150 Calories at rest. However, in the same amount of time you burned another 1350 Calories you otherwise wouldn't have. That makes your total Calorie expenditure for the day 3750 Calories (the net from exercise + the BMR). We haven't even factored in your normal activity level to adjust the BMR to what your body would need to maintain it's current weight. Nor have we factored in what your body needs to recover from that training.
In short, eat up on training days. As long as you have your required amount of protein in the day, fill in the remaining Calories you need with what you like. The body will be remarkably tolerant of Carbs and fats after intense training sessions.