The 19-year-old moved to Goodison Park on transfer deadline day from Hajduk Split, having caught the eye while playing against the Toffees in the competition's playoff round earlier that month.
Vlasic made his debut for his new side towards the end of their 3-0 loss to Tottenham Hotspur on Saturday but could get his first start when Ronald Koeman's side play their first game of the Europa League group stages at Atalanta tomorrow night.
"I'm really looking forward to it," Vlasic told the Everton website. "I've never played in the group stage of the Europa League before, so it's exciting. It is something new and a good challenge.
"We need to forget about Saturday's loss to Tottenham and look ahead, prepare ourselves and I hope we can get a good result.
"All the guys have been very good to me, they are all helping me a lot. I watched these players before on television and now I'm out on the pitch with them. I can only learn from them because they are very big players.
"It is very fast football here. The game moves faster and I need some time to adapt but I'm not afraid."
During his four seasons with Split, Vlasic racked up 120 first-team appearances in all competitions, scoring 13 goals.