The Toffees made a strong start to the new campaign with a 1-0 victory against Manchester United on Monday, and Jelavic thinks that performance can be the catalyst for a fantastic season.
He told Croatian newspaper Vecernji: "We can aim high, not only because of this victory but because we have a really good team.
"We are like one big family and we also signed some great players this summer. You could all see at the United game that we are really strong this season.
"United are strong but we killed them. David de Gea saved them, we could have really destroyed them. We can be really optimistic now."
Everton play their first away game of the season against Aston Villa on Saturday, August 25.