Your problem is with the vendor rather than the strata manager, as it appears you bought two things – the apartment and the carspace lease. The vendor should have provided you with everything you needed to effect the transfer of the lease into your name at the same time as the apartment was transferred. If they have not done that, presuming you have paid the vendor, then you should pursue them for specific perfomance of the contract.
I suggest you speak to the person who handled the settlement of the property as a matter of priority. You may need to seek legal advice.