The Ghanaian revealed ahead of the game his ambition to at least send one ball beyond goalkeeper Petr Cech but failed to achieve it.
The 23-year-old wasted a glorious opportunity to take the lead for the Serbian side before the break, after racing in behind Rob Holding on a swift counter-attack.
With nine minutes remaining, the former Juventus striker fluffed arguably the biggest chance of the game to win it for his side, when he was played through by a teammate but saw his last ditch effort go wide.
English-born of Ghanaian descent Eddie Nketiah was brought on by Arsenal for Willock in the 68th minute, but the youngster couldn't repeat his heroics in the EFL.
The stalemate means that Zvezda have become the first Serbian side to keep a clean sheet away from home against an English opposition since FK Partizan's 1-0 victory over Newcastle United in August 2003.
Arsenal have qualified to the next round of the competition but Zvezda sit second and will have to shrug off the challenge from FC Cologne to pick the other ticket after the German side claimed a 5-2 away victory over BATE Borisov.