Just keep up the pace man! I recently started Kickboxing and have had the reverse problem. It was weird to me that I could roll back to back Jiu Jitsu classes but was getting gassed in kickboxing sparring. Talked to a few of my coaches and a few things came up like The pace is different, my body wasn't used to it yet, etc. When I do kickboxing it seems like there is an anaerobic element to it but it seems like it taps into the aerobic more, in Jiu Jitsu There is definitely aerobic and anaerobic elements but I always feel like I've taxed the anaerobic system more after rolling. If you have been doing stand up arts for a while and are already in good shape for those arts, Than this is probably going to be a sport specific thing, where you need to work on sport specific conditioning. I've seen guys who were in good shape go to their first no gi class and get gassed. After a couple weeks if they stay consistent (about 3-4 days a week) their conditioning gets real good because they already had a good base to build from. Also out of curiosity how hard are you rolling on a scale of 1-100% ? Energy efficiency/conservation is a big thing, When I first started out I used to get gassed all the time because I was going balls to the wall every round like it was the championship or something, once I learned how to conserve my energy and not spazz things got better.
At this point Going to class and sparring, and spending as much time on the mat will help the most. If you want some extra work solo drills, If you got a heavy bag I have one on the floor at my house where I practice moving from position to position,side control,knee on belly,mount,kesa gatame/reverse kesa,north south, drilling armbars from mount etc There are some good videos on solo drills on youtube but thats all supplemental it will help your movement and cardio to a degree but sparring is #1