The former Chelsea striker issued a warning to the Gunners after a draw in the first leg.
Ba twice came close to scoring against the Gunners in a tense first leg in Istanbul which ended in a 0-0 draw.
The former Chelsea man hit the crossbar with an audacious strike directly from kickoff, which was kept out by the fingertips of Arsenal goalkeeper Wojciech Szczesny.
He later almost capitalised on a mistake by 19-year-old centre back Calum Chambers, cutting inside before dragging his shot wide when through on goal.
Ba believes Besiktas came close to getting a result against the Gunners, and issued a warning to the North London club ahead of the return fixture.
"Sometimes you have these kind of games," Ba said after the match.
"We created chances but couldn't finish them off, it was a commendable performance, there wasn't a lot missing it was just the little things we couldn't pull off at the end of the night.
"But in London we won't be as wasteful in front of goal, we aren't going to London to see Big Ben, we are not tourists going on a sightseeing tour.
"After our performance tonight Arsenal will take us more seriously, the Emirates will be full but this doesn't really bother us. We showed what we are capable of."
Arsenal will head into the second leg without perhaps their most important player after Aaron Ramsey was sent off for a second bookable offence late on.
The Gunners will be confident that they can pick up a win on home soil against the Turkish side, but if Ba is able to grab an away goal in his return to London it could make this an uncomfortable tie for Arsene Wenger's side.