Roger Schmidt's men ultimately proved too wasteful in front of goal during Tuesday's Group C clash at the Stade Louis II, with Bellarabi, Gonzalo Castro and Son Heung-min all spurning decent opportunities.
Monaco eventually broke the deadlock in the 61st minute when Joao Moutinho latched on to Dimitar Berbatov's knock-down before seeing his effort deflect off Emir Spahic and over Bernd Leno, easing the pressure on coach Leonardo Jardim.
The Ligue 1 side looked more likely to net again in the later stages and Bellarabi was left under no illusion that Leverkusen must improve in front of goal.
"We had to convert our big chances in the first half, of course," said the winger.
"Otherwise we wouldn't have lost the game. We have to learn from that game."
Schmidt was understandably angered by the result and, although he praised his defensive unit, he was not so certain about suggestions that his team were better than Monaco on the night.
He added: "If you are so superior, you should express that in the result. I am very bitter, because we stood very well defensively and allowed little through.
"But, it was only one of six games in this group."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.