Before the end of the transfer window, Vlasic was signed from Hajduk Split after impressing Ronald Koeman in the Europa League tie between the two clubs in August.
Vlasic came off the bench in Saturday's 3-0 defeat to Spurs and while admitting that he was delighted to feature for the Toffees, the young Croatian has acknowledged that he did not enjoy the perfect day.
The 19-year-old is quoted by the Liverpool Echo as saying: "There's a lot of emotions. It was a very special moment for me.
"I was happy when the crowd clapped me as I came on but on the other hand, I'm sad because we lost the game."
Earlier this year, Vlasic made his international debut for Croatia, despite only leaving his teenage years last October.