Yes, that´s right!
So, your sentence would be ''I could not handle that problem."
Notice that in use, in Dictionaries of collocations. http://www.ozdic.com/collocation-dictionary/handlehttp://oxforddictionary.so8848.com/search?word=handle
In the last example they point out that one can use preposition in a sentence, only that in immediatelly after the word/verb "handle":
She handled the crisis with total assurance.
Plus , generally someone writing will use the preposition with
in the sentence, not other.
Of course, there will be a few cases in wich the preposition we can use other prepositions:
as in - For simpler cases, detoxification and medical care will be handled by the in-house medical team.
That´s why in English we have to heed tha advice of Justin Bieber song never say never! But with practice, we will know wich cases requires wich preposition.