Frank Lampard said Chelsea need to cut out individual errors after they twice relinquished a lead to draw 3-3 with Southampton.
Jannik Vestergaard headed in a dramatic injury-time equaliser to claim the Saints a point, after Danny Ings and Che Adams had earlier brought the visitors back from 2-0 down to 2-2 at Stamford Bridge.
All the goals conceded by the Blues included defensive mistakes, with Kai Havertz needlessly losing possession in his own half for the first, a weak back-pass from Kurt Zouma and poor attempted block from goalkeeper Kepa Arrizabalaga contributing to the second, and an unnecessarily conceded free-kick and poor attempted clearance enabling the third.
"We have to not give those goals away," Lampard told BBC Sport. "We are making individual mistakes in games and it gives other teams chances at all times. It is something we need to get better at.
"It goes through the team. We are seeing a lot of goals in the Premier League at the moment and no manager is happy with that. We all want clean sheets. It has to be better."
Chelsea were in control courtesy of two superb Timo Werner goals - the first courtesy of a sublime dummy which bamboozled Jan Bednarek before drilling in, and the second as he lobbed the ball over goalkeeper Alex McCarthy and nodded home.
When it looked like the hosts were cruising, Southampton hit back as Danny Ings went round keeper Arrizabalaga to finish and Adams punished dire Chelsea defending to smash home an equaliser.
The Blues responded just 121 seconds later with Werner sliding the ball across the box for compatriot Kai Havertz to convert an easy finish which seemed to be the winner, but Vestergaard's late effort sealed a draw.
"You go 2-0 up and you want to finish the game, as at that point we were playing great football. The first half was as good as we have played this season," added Lampard.
"Southampton are a good side and we allowed the pressure they want to put you under off the ball to gain traction.
"When they got their first goal, just before half-time, they put us under pressure and our game management could be better.
"My message at the break was that it shouldn't change the game and the players should be happy with how they have played for 40 minutes. But we never reached those levels in the second half."
Chelsea's defensive frailties prove costly
Despite a top-four finish last season, the problems for Frank Lampard's side were obvious - weak at the back, they paid a heavy price for their frailties against Southampton.
Chelsea conceded 54 goals last term, more than any other team that finished in the top 10, but a heavy spending spree in the summer invested more in attacking additions than defensive reinforcements.
The experienced Thiago Silva, brought in on a free after leaving Paris St-Germain, missed out and goalkeeper Edouard Mendy suffered an injury on international duty with Senegal.
It meant the error-prone Kepa was back in goal and his contribution for Southampton's second goal was far from impressive, but he could do nothing about their equaliser.
Lampard insisted that he and the team have faith in the keeper, but it will require hard work and mental strength from the 26-year-old to rediscover his form.
"He has to be strong enough mentally; that's the job we're in," said Lampard. "He has to deal with that, he has the support of myself and his team-mates.
"He has to keep working, that's the only way through it. It's unfortunate because he did make two really good saves today, but obviously with something like the second goal, then eyes are drawn to that."
The home side failed to capitalise on champions Liverpool's 2-2 draw at Everton earlier on Saturday, with them missing out on the chance to go second and instead staying sixth.
But while they work on resolving their backline problems, they will have no problems going forward with the fire power they possess.
Prolific striker Werner looked like heading to champions Liverpool but the transfer did not materialise and he showcased why Chelsea were quick to pay £54m for the RB Leipzig man.
Werner, who scored 34 goals last season, was a constant menace for the Saints backline, his low centre of gravity allowing him to shift left and right, bringing about the first goal.
He had his back to goal a long way, but his step-over and dart left Bednarek trailing and, despite having work to do with three defenders and the goalkeeper in attendance, Werner slipped a cool finish into the bottom corner.
Werner caused problems for the same defender for the second goal, holding off the towering Bednarek from Jorginho's raking pass, calmly lofting the ball over the advancing McCarthy and heading in from close range.
Chelsea's dangerous trio of attackers combined for the third as Christian Pulisic found Werner's run into the box and he moved it on for Havertz's first league goal.
With Hakim Ziyech making his debut off the bench in the final 18 minutes, as well as the options of Tammy Abraham, Olivier Giroud and Callum Hudson-Odoi available to Lampard, Chelsea will not have problems scoring goals.
It is at the back where they remain most vulnerable.