It’s your coach’s responsibility to ensure that you know what you should be working on and the elements to focus on.
However, ultimate responsibility of your improvement lies with you. You are the one who actually has to do the hard work and put in the hours of training – and yes, they will be hours.
Ideally, you should work WITH your coach in ensuring your training without him or her is beneficial.
If necessary, ask him or her for at least one, preferably two and at most three things that you should be paying attention to when you are playing, pairs/group practicing or doing solo routines.
Then make sure you report back. If he or she doesn’t ask, tell your coach what happened and discuss ways to improve your next sessions without him or her.