Slightly longer

Rebekah, if you're American like me, I suspect that your teacher's point may have been that it's important to pronounce the first vowel of OMICRON more like an "O" than like an "A".

That is to say, for most Americans the stressed "O" in "doctor" sounds more like the Greek ALFA in DHAKTILA 'finger' than like the Greek OMIKRON in the first syllable of DHORON 'gift' (I welcome corrections to my Greek and instructions on how to enter text in Greek script). Similarly, we pronounce "Mom and Pop" with vowels close to the ALFAs in I MANA KE O PAPAS. So many Americans tend to mispronounce the "O"s in other languages (I've heard of a Mrs. Oporto addressed as "Mrs. Aborto"--'Mrs. Abortion'). Maybe this was what your teacher had in mind, rather than a more subtle distinction between a more or less open "O", or a longer or shorter one.

for Patricia
if o-mikron is pronounced as in 'poke', then o-mega is either pronounced as in 'poke', without a difference, or held slightly longer and lower in the mouth toward 'aw' in some dialects of English.
if you are aiming at KOINH, then o-mikron and o-mega are pronounced the same, just like in modern Greek.