Guus Hiddink was targeting a strong season finale for Chelsea after a 2-1 win at Carrow Road which sent Norwich into the relegation zone.
Chelsea climbed to eighth, five points behind fifth-placed Manchester United and eight adrift of fourth-placed Manchester City with their third straight Premier League win, which came amid controversy as Diego Costa’s decisive goal came from an offside position.
“We have now won a few games in a row. We have to keep on winning,” the Chelsea interim boss said.
“Now with the ambition of Chelsea we must set a new target and see what we can do in the direction of Europe.
“If everyone is on board and there are no big injuries, we’d like to go as high as possible towards European spots.”
Chelsea scored after 39 seconds – Kenedy netting the fastest goal of the Premier League season so far – before assistant referee Michael McDonough failed to flag and referee Lee Mason awarded Costa a second.
Hiddink felt Chelsea should have built on Kenedy’s opener before Costa’s strike.
“We had a splendid start from Kenedy, a beautiful goal. After that we had options for a second,” Hiddink added.
“We should’ve killed it off already. I’m satisfied about the result, but I like to always be a bit more critical. We were a bit sloppy in finishing off.”
Norwich ensured Chelsea never truly had a grip on proceedings and had the better of the second half. Cameron Jerome hit the bar early in the second half and Nathan Redmond pulled a goal back 22 minutes from time, but it was too little, too late.
Norwich boss Alex Neil lamented familiar failings in a seventh loss in eight Premier League games.
“(Kenedy) is offside. I’ve seen it back on the video,” Neil said.
“You would expect the officials to get it right. It’s disappointing they don’t get it right. They’ll be disappointed they didn’t get it right. But the linesman’s called it how he saw it.
“It’s not as if he’s two or three yards offside. He’s probably a yard, half a yard. You’d like to think he would’ve got that one correct, but when you’re down at that bottom end those wee bits of fortune that you look for just don’t come your way.
“It’s probably been the story of our last few games. We had better opportunities than Leicester, lost the game. West Ham we were 2-0 up, looking comfortable and we managed to draw. Liverpool we were 3-1 up and managed to lose the game.
“When that’s a continuous thing that keeps happening, I don’t think it boils down to just luck. Quality shows and at times we missed opportunities we should’ve taken.”
Midfielder Alex Tettey went off in the first half for a precautionary X-Ray on a leg injury and Gary O’Neil required stitches to a two-inch gash on his head following a clash with team-mate Robbie Brady, who lost two teeth and chipped another.