Hello,
Your inventory cannot be expanded. However, it should be large enough to hold all the items you need to play the game. Perhaps try opening some of the packs you are holding on to?
Thanks!

You cannot expand it. You need to use what you have in order to make more space. First you should spend anything that you have a really low amount, if possible. Such as merging some of your magatamas, if you only have few of some of them. Using Cultivate Scroll since it doesn't count towards rebate. Using tactic pages if you have any from Wanted Missions. Selling mining ores. Etc.

Once you have a few slots open, you should be able to open packs again. So then start opening packs to make room such as Cat Quiz, Ninja Optional, etc. Then again, use things that end up clearing out a spot completely. Just keep repeating this process until you have enough spots open. Then everything should go back to normal. And try to pay attention for next time. Anytime you get a lot of items, start using or merging them to take up less spots to avoid this happening again.