The Croatia international's second-minute goal was enough for CSKA to stun reigning champions Madrid 1-0 in Group G.
"It was probably the biggest match of my career so far," he said, via UEFA .
"Do Everton regret letting me leave on loan? I wasn't getting to the team so I came to CSKA and am very happy to be here and playing in big games like this."
Vlasic produced a clinical finish for the game's only goal, and CSKA – who had goalkeeper Igor Akinfeev sent off late – managed to close out a famous win.
After scoring his third goal of the season, Vlasic said his side deserved their victory.
"Of course we believed," he said. "We went into the game like there were no names. We went into the game thinking they are only people like us.
"Of course they are very good footballers but we believed in ourselves, and I think it's easier when you approach it like that.
"You don't look at names and you are not scared, and we did that."
The win helped CSKA move top of Group G with four points, sitting ahead of Madrid and Roma.