Owing to a brace from Callum Wilson, Bournemouth thrashed Everton 3-1 in their backyard at the Dean Court stadium on Sunday.
Ryan Fraser scored the remaining goal for Everton, whereas Calvert-Levin scored the solitary goal for the guests.
Post their loss, Everton manager Marco Silva told talkSPORT: “It’s a big frustration for us, a big frustration because it’s not something you do just one day during the week, it’s something that’s part of our weekly plan.
“We took some time to settle and address everything last season, but after we addressed it, we went so many games without conceding goals and giving so easy things to our opponent.
“We came here and conceded again. Like I said it’s better to be aggressive and active and challenge that moment. It’s a big frustration. We know what our opponent does, we were prepared, but we came here and didn’t do enough.”
Meanwhile, at Vicarage Road on Sunday, Watford played 2-2 draw with Arsenal.
Earlier in the match, Pierre-Emerick Aubameyang scored twice to give Arsenal a 2-0 lead in the match, but later the Gunners squandered the lead as Watford hit back to draw 2-2.
In the 53rd minute, Tom Cleverley halved the deficit for Watford after some dreadful Arsenal carelessness. The home side got their second goal after being awarded a penalty which was converted by Roberto Pereyra in the 81st-minute.