The Blues took on the Gunners at Stamford Bridge for a highly-anticipated Premier League fixture. Thomas Tuchel's side were in better form heading into this contest, with their opponents having suffered three successive league defeats prior to the match.
However, a litany of individual errors from both sides eventually ended with a 4-2 win for Mikel Arteta's side.
Speaking on Sky Sports after the match, Hasselbaink said:
"Lukaku, Christensen, Sarr and Alonso - they were just not good enough for a Chelsea team that should be challenging for winning the Premier League. I know they can't be No. 1 anymore but you still play for your pride."
While Lukaku had no shots on target and just 22 touches during his 60 minutes on the pitch, Christensen made the error that gifted Arsenal their opener.
Sarr, who started in place of the absent Antonio Rudiger, and Alonso struggled against Bukayo Saka's pace down the left side of the defense.
In his post-match interview, Tuchel refrained from naming specific players, but Hasselbaink believes the German will be disappointed with some individuals.
The former striker added:
"I think Tuchel is very disappointed. I don't think he wants to be too critical of individuals but I think he's very disappointed in certain individuals."
Hasselbaink also critiqued Tuchel's comments about the playing surface at Stamford Bridge not being up to scratch (as per Metro), stating:
"I don't understand why he's talking about the pitch because there's two teams playing on the pitch. Maybe he's trying to protect certain individuals but if you look at the game, Chelsea were well under par."
Cesar Azpilicueta and Andreas Christensen record poor outings as Arsenal beat Chelsea
Chelsea got off to the worst start possible when Andreas Christensen's awful back-pass was intercepted by Eddie Nketiah. The Arsenal forward ran towards goal without a defender in sight before slotting home comfortably past Edouard Mendy in the 13th minute.
The Blues got back into the game through Timo Werner's deflected strike from an Arsenal mistake just four minutes later.
However, more questionable defending and some individual brilliance from Emile Smith Rowe saw the Gunners take the lead.
Cesar Azpilicueta then arrived at the back-post to score from Mason Mount's clipped pass, leveling the scores once again before half-time.
However, the Spaniard's error allowed Arsenal to collect a loose ball in the build-up to Nketiah's second goal to put the visitors up 3-2 in the 57th minute.
Azpilicueta's mixed outing reached a dramatic conclusion when he clumsily and needlessly fouled Saka inside the box to gift away a penalty. The Englishman sent Mendy the wrong way to seal the win for Arteta's side in stoppage time.
The win took Arsenal level on points with fourth-placed Tottenham Hotspur, who remain narrowly ahead on goal difference. The Gunners are now three points clear of fellow top-four aspirants Manchester United, while also having a game in hand.