Chelsea climbed into the top four after beating Newcastle and Frank Lampard challenged them to stay there.
Marcos Alonso's goal 17 minutes from the end secured a 1-0 victory and moved the Blues into the Champions League spots for the first time this season.
"It sounds good," said Lampard. "We know we want to be challenging in the top four and from a slightly difficult start it's a good sign that we are moving in the right direction.
"But our arrival in the top four must give us the hunger to stay there."
Chelsea had struggled to break down a stubborn Newcastle side until the introduction of Christian Pulisic as a substitute.
The £58million United States winger missed a sitter when he fired straight at Martin Dubravka from six yards, but a few minutes later he played a central role in the goal.
Pulisic burst forward into the penalty area and pulled the ball back for Callum Hudson-Odoi, who touched it on for Alonso to drill home.
"I'm really pleased for him," added Lampard. "He's a bit of a hot topic because of his price tag and international status, but he's just turned 21. There's a lot more to come.
"In the first half we were a bit safe, and a bit slow, we didn't have enough urgency. That was the message at half-time, and in the second half we should have had more goals and made the win more comfortable.
"I thought particularly in the second half we saw the spirit and energy in the team. We have to go back to basics. Today was tough, we had a problem in the game, but we solved it in the second half.
"The players need to be brave and confident and it's a great sign in the squad when players come on and make a difference."
Newcastle boss Steve Bruce felt there was a foul in the build-up to the goal.
"I know it's a difficult job but I thought there was blatant foul on Joelinton, in front of us, and we never retained the ball after that," he said.
"When you come here you need those sorts of decisions to go your way and not against you
"Up until then we gave as good as we got, but the most important thing for us to work on is at the top end of the pitch.
"We've had a really tough start but now we have a run of games against teams in and around us, so it's a vitally important time."
Chelsea midfielder Ross Barkley limped off before half-time after turning his ankle and he will be assessed on Sunday.
