After «несколько», you use the genitive.
Showing ownership is just one of the functions of genitive.
a) хоте́лось (and it's present-tense form, хочется) is an impersonal form, unlike хочу, so you need dative case (мне 'to me') and not nominative (я),
б) хоте́лось is a past tense,
в) был is a past tense marker which is not needed since хоте́лось is already in the past tense (also, it's ungrammatical because it refers to я and хоте́лось is an impersonal form, so you can't use я, only мне); and the English sentence is in the Present tense.
«Мне хо́чется сказа́ть не́сколько слов» should be accepted.
"a couple words" meaning "a few words" is very colloquial English. People use it as a synonym for "a few", but that's not accurate. It reeks of false humility, too, because you just know the person is not going to say just two words - or probably not just 20. It's also a kind of slang. Not really appropriate here.
To share some research:
несколько can function as a pronoun (Wiktionary) meaning "a few, several, some [+ genitive]" (the use in this exercise), (for declension table, see: https://en.wiktionary.org/wiki/%D0%BD%D0%B5%D1%81%D0%BA%1D0%BE%D0%BB%D1%8C%D0%BA%D0%BEor)
or as an adjective meaning "a few, some, several" (Katzner's Russian-English Dicitonary)
or as an adverb meaning:
- somewhat, slightly, rather; some
- multiple, a couple