The Croat was handed a start in the defeat at Goodison Park following his impressive contribution off the bench against Apollon Limassol in the Europa League last Thursday.
Vlasic was a revelation against the Cypriots and scored what almost proved to be the winner with a second-half strike but it was he who switched off the allow Steven Ward behind him in the Premier League game against the Clarets to provide the winning assist for Jeff Hendrick.
The 19-year-old wasn't shying away from his mistake and he accepts it's part of the learning process for a young player at a new club.
“It is very disappointing because we started the game very well,” Vlasic told evertontv.
“We had chances, we pushed them into their defensive 60 metres but we made one or two mistakes and conceded a goal.
“In the first half, yes [I was happy with my performance], but the goal… I was part of that mistake. I am very sad about that but I gave it my all and I wanted us to score the goal to earn a point. I wanted to win but after 1-0 you need to score two goals.
“I am very disappointed about that. But I believe in this team. I think we are very good players and we have a good manager.
“Sometimes in football, you have luck, sometimes you do not. In the past few games we had many opportunities but did not score and if the opposing team had an opportunity they scored.
“In the future, it will be better.”