Sure, eat enough extra to support the cardio. Then do 15 or 16 minutes doing ALL YOU CAN DO for your chosen
cardiovascular exercise. Then you won't burn off your gains AND you'll give your heart a workout.
Feed cardio just like any other workout - Keep the gains, keep them lean, have a healthy heart.
But I think if you are putting out maximum effort on a lift - it is likely going to leave you short of breath anyway. Those muscles need oxygen to work. Bigger muscles need more oxygen than smaller ones. When a part of the body has an increased oxygen demand, one will feel short of breath, increase respiratory rate and tidal volume. Then the heart rate increases to carry plenty of oxygen enriched blood to where it is needed.
That's why you see Lance Armstrong instead of Ronnie Coleman winning all of those l o n g bicycle races.
Smaller muscles need less oxygen and don't tire nearly as quickly so they have more endurance.
Edit: 3N beat me to the submit button.
oops.