The Croatia international has stressed that Bayern Munich cannot afford to take the Gunners lightly despite the club's advantage heading into the second leg.
The Bavarians recorded a 3-1 away win in the first leg, and Mandzukic is confident that the team will progress if it can put in a similar performance; however, he has warned that the tie can go either way if Arsenal gets an early goal in the second leg.
"A lot of people think we’re already through to the next round, but anything can happen in football," the Croatia international told the official Bayern website. "Provided we play the way we did in London we need have no worries.
"Nevertheless, if we concede an early goal, it could be dangerous."
The 26-year-old Mandzukic, enjoying his first season with the current Bundesliga table-topper, then went on to voice his delight with his goal in the away match versus Arsenal.
"I'm obviously delighted about the goal, partly because it was an odd one. The press were saying I lacked a goal in the Champions League, but I never let it get to me. The only thing that ever matters to me is winning."
Mandzukic has already netted 19 goals in all competitions for Bayern this season.