This was hardly the emphatic response Frank Lampard had hoped for and, as he highlighted with a whiff of exasperation, when Marcos Alonso again proved the saviour, this time to rescue a point with five minutes left on the clock at Bournemouth, there should inevitably be questions raised. Alonso ensured a Chelsea team depleted by injuries – particularly in forward areas with Tammy Abraham sent to Barcelona to see a specialist regarding his ankle injury – did not depart empty handed, heading in an equaliser to help hold on to fourth spot for at least another week after Chelsea fell behind to goals from Joshua King and Jefferson Lerma in three remarkable second-half minutes.

Lampard did not attempt to sugarcoat a humbling defeat by Bayern Munich in midweek and acknowledged that his side, who host Liverpool in the FA Cup fifth round on Tuesday, were below-par in both boxes again here. “Marcos Alonso has had a big week but I don’t want my left-back top of the scoring charts,” Lampard said. “I want our attackers scoring goals and they haven’t.

“When I think that my left-back is the one scoring the two goals and the one who scored our last goal in the league [against Tottenham], and we are creating that many chances in between, you have to question why we are not finishing them. We are fighting for fourth against teams that are pushing the same as us and we really are striving for a little run of form where it’s win, win, win. That’s where we haven’t been for a while and that’s why we have to really dig in at the moment and find wins because if you have 73% possession, 23 shots and you don’t win the game, there are question marks in both boxes, without a doubt. That’s been a constant for us.”

Bournemouth dominated the opening stages, exposing Chelsea’s wing-back system with Ryan Fraser releasing the overlapping full-back Jack Stacey, who cut the ball back for Philip Billing. It was an inviting cross but Billing, languid in style, lacked conviction and toe-poked the ball straight at Willy Caballero, who was again preferred to Kepa Arrizabalaga in the Chelsea goal. Billing had a chance to make amends seconds later when Fikayo Tomori, who was withdrawn an hour into his first league start since December, failed to control a loose ball. Billing sensed an air of vulnerability and seized possession but hammered a left-foot shot into the side netting.

As it happened that wing-back system provided a platform for Chelsea to build on when Alonso opened the scoring, but its pitfalls were laid bare when Billing slipped in Stacey, who rampaged into the 18-yard box and slid a wonderful ball across goal.

It eluded Callum Wilson’s outstretched left boot but not King, who was on hand to tap in at the back post and give Bournemouth the lead after Lerma towered above Mateo Kovacic to head in an equaliser from Fraser’s corner. Then, a week on from having two goals chalked off in defeat at Turf Moor, came another agonising VAR check, with the referee Andre Marriner waiting for the video assistant referee’s verdict back at Stockley Park. King was ruled onside and Bournemouth had stung Chelsea.

Bournemouth’s Joshua King scores their second goal. Photograph: Peter Nicholls/Reuters

Chelsea, who had controlled large spells, were suddenly pegged back, prompting Lampard to introduce Ross Barkley and Willian off the bench. Michy Batshuayi soon followed in place of Olivier Giroud. Barkley replaced Jorginho, who will serve a two-match suspension after picking up a booking here. Batshuayi had the ball in the net less than a minute after entering but the striker was offside.

Then César Azpilicueta thrashed the ball wide as panic ensued in the Bournemouth box, but they eventually found a way through when the Chelsea captain picked out Pedro, who forced a superb right-hand save from Aaron Ramsdale, only for the rebound to drop kindly for Alonso.

Things do not get any easier for Bournemouth, who slipped into the relegation zone after Watford’s shock win over Liverpool and face a trip to Liverpool next Saturday but, as it may for Chelsea, this may prove a valuable point. “In really tight games, if we’re not going to win them, we need to draw them,” said Eddie Howe, the Bournemouth manager.

“But when you’re winning so late in the game, you’re craving three points and desperate for three points, so there are mixed emotions. We are not where we want to be in the table and it is going to be a battle but I am seeing signs that the team is ready for the challenge.”