The Costa Rica international is on loan at the Greek club from Arsenal and speaking to ESPN Deportes after the victory, he admitted he still has one eye on his future back in the Premier League.
He said: "I am still hopeful of playing for Arsenal but I have not been given the chance yet, I hope to keep working at Olympiakos.
"I am making sure that I take this opportunity."
The Greek champions thoroughly deserved their victory against a poor United side, but Campbell said there is still work to be done in the return leg at Old Trafford in three weeks' time.
He added: "We played every well against a very good team and we weren't intimidated.
"There is still a very hard game at Old Trafford and we hope to advance to the next round.
"Thank God I scored a goal and celebrated it with my father, girlfriend and cousins.
"There are many things I can improve on though, I am 21 and I have to keep working."