Antonio Conte warned Chelsea's top four rivals that his side will fight to the finish as the race to qualify for the Champions League goes down to the wire.
Olivier Giroud boosted Chelsea's bid to snatch a top four place as the France striker sealed a 1-0 win over Liverpool that brought the Champions League finalists back down to earth.
Giroud's first-half header at Stamford Bridge lifted fifth-placed Chelsea to within two points of fourth-placed Tottenham in the race to qualify for next season's Champions League.
"Usually when you play a must-win game it is not easy because it's normal to be a bit nervous," Blues boss Conte said.
"We had the will to win, to keep the hope alive that we can get a place in the Champions League.
"I don't know if this will be enough at the end of the season but we have to try."
In a dramatic conclusion to the top four battle, Chelsea, who are three points behind Liverpool, host struggling Huddersfield on Wednesday and Tottenham face Newcastle the same evening.
On the final day of the season next Sunday, Chelsea head to Newcastle and Tottenham entertain Leicester.
"It's important to face this situation with a lot of pride and show we are still alive," Conte said.
"Probably one month ago it was impossible to imagine we would arrive at the end of the season fighting for the Champions League.
"We are winning and our opponents are dropping points. We are putting pressure on the other teams."
It was a frustrating return to domestic action for Liverpool after their Champions League semi-final success against Roma in midweek.
With only one win in their last five league games, third placed Liverpool have made their top four status an unnecessarily tense affair.
"I hate the result. The performance was good enough to get a good point, but we weren't clinical enough," Liverpool manager Jurgen Klopp said.
Klopp's team should still be able to guarantee a Champions League berth if they beat Brighton at Anfield on Sunday.
- Revised plans -
Even if they don't finish in the top four, Liverpool can return to Europe's elite club competition by defeating Real Madrid in the Champions League final on May 26.
"When I woke up this morning I was hoping for a 3-0 win, so we didn't have to care about the Brighton game and could start to prepare the final. Did I think it would happen? I'm not sure," Klopp said.
"Chelsea has to win as well. We play at home in our last game, they play at Newcastle. That doesn't sound like a holiday to me.
"Brighton is a very important game for us, but we've had a few of them in the past and they haven't been too bad."
Klopp also condemned Liverpool winger Mohamed Salah for a dive that earned him a booking.
"That's not what I want to see and not what he wants to do," he said.
Liverpool had made a bright start and Roberto Firmino tested Thibaut Courtois with a dipping half-volley.
Sadio Mane's 25-yard drive forced a sprawling save from Courtois and from the resulting corner, the Chelsea keeper needed to be alert to stop Virgil van Dijk heading in from close range.
Mane was in a personal duel with Courtois, who kept out another powerful blast from the Senegal winger, then scrambled to his feet to deny him again from the rebound.
But despite their pressure, Liverpool were caught with a sucker punch in the 32nd minute as Giroud justified Conte's decision to select him at the expense of the out of form Alvaro Morata.
Victor Moses teased Andrew Robertson as he worked space to swing over a cross and Giroud, stealing in front of the slow to react Dejan Lovren, glanced a fine header into the far corner of the net.
Giroud celebrated his fifth Chelsea goal since his January move from Arsenal by sprinting over to the bench and clambered up to hug team-mate David Luiz, who wasn't involved in the matchday squad.
Olivier Giroud has scored four goals in his last five matches for Chelsea after a slow start