The Croatian midfielder opened the scoring in the 15th minute before teeing up Tasos Douvikas for Como's second, and spoke to UEFA pitchside afterwards about the significance of the night.
"It's an incredible feeling to have scored my first Champions League goal with Como, but it's down to the whole team. We showed great intensity out on the pitch," Baturina said.
"We prepared for the match like we would for any other game. We didn't want the Champions League atmosphere to affect us too much, so we focused on our usual preparation."
UEFA's technical observers explained their reasoning for handing Baturina the award, praising his all-round contribution to Como's dominance.
"He scored the first goal and provided the assist for the second with a great pass. His intelligent movement created a numerical superiority in midfield, allowing his team to dominate the match," the panel said.
Baturina also reflected on what the win meant beyond the pitch itself, in what was Como's first appearance in a UEFA competition.
"I'm very happy and proud that we won our first Champions League match. I'm sure the whole city is very happy, and now we can celebrate," he said.
The 23-year-old has quickly established himself as one of Cesc Fabregas's most important players since arriving in Italy, and Thursday's performance — decisive both in front of goal and in controlling the tempo of the match — underlined why. Baturina joined Como from Dinamo Zagreb last summer in a club-record deal worth around €25m including bonuses, having previously been the subject of interest from Newcastle United, Nottingham Forest and Inter Milan before choosing the move to Lake Como.
Como went on to complete the 4-1 win with further goals from Assane Diao and Maximo Perrone, sealing a dream start to their first-ever European campaign at the Stadio Sinigaglia.
Attention now turns to Monday's Serie A home fixture against Parma, with Baturina expected to remain a central figure in Fabregas's plans as Como look to carry their momentum from Europe into the domestic season.