A third consecutive win lifted Everton four points clear of the relegation zone as the Toffees continue to shrug off a 10-point deduction for breaches of financial rules.
Abdoulaye Doucoure opened the scoring before Lewis Dobbin's first Everton goal imposed another damaging defeat on Pochettino.
Without the penalty for breaching financial rules, which Everton are appealing, Sean Dyche's men would be four points above Chelsea in mid-table.
A seventh defeat in 16 league games in charge for Pochettino sees Chelsea slip into the bottom half, behind west London neighbours Fulham.
"We need to analyse the reality. We need to talk and to try to improve in the next transfer market," said Pochettino.
It was a familiar story for Pochettino as Chelsea dominated the game but failed to make it count.
For the third time this season Chelsea lost despite enjoying over 70 percent possession.
"Football is about scoring goals and we were not clinical in front of goal," added the former Tottenham boss.
Pochettino has pleaded for patience as he tries to mould together an array of expensive young talent.
But Chelsea managers do not tend to get much time to turn things around and the pressure is on the Argentine to find a quick fix to his side's problems.
Pochettino shuffled his pack after a dreadful display in losing 2-1 at Manchester United in midweek.
Chelsea were able to welcome back Conor Gallagher from suspension, while captain Reece James, Benoit Badiashile and Armando Broja came in as Pochettino made four changes.
But James' injury-hit campaign goes on as he was forced off midway through the first half.
Chelsea were undone by a familiar lack of punch up front.
Enzo Fernandez tested Jordan Pickford with an effort from outside the box before the England number one produced a spectacular stop to deny Cole Palmer a stunning goal from long range.
Broja was offering far more than Nicolas Jackson as a target for Chelsea to hit, but did not solve Pochettino's need for a clinical finisher.
The Albanian prodded his best chance over late in the first half from Mykhailo Mudryk's teasing cross.
Everton find groove
Everton blew Newcastle away 3-0 to move out of the relegation zone on Thursday but took time to warm to their task.
It was not until after half-time that the hosts had a shot on target as Dwight McNeil's sweet strike from the edge of the box was turned behind by Robert Sanchez.
Chelsea did not heed that warning as they were cut wide open with Everton's next attack.
McNeil's pass in behind was perfectly weighted for Dominic Calvert-Lewin and when his effort was saved by Sanchez, Doucoure was on hand to fire in the rebound.
The Mali international scored the goal on the final day of last season that saved Everton from relegation and his six goals already this season are going a long way to prolonging their 70-year stay in the English top flight.
Everton then comfortably held on before adding to their lead in stoppage time.
Chelsea substitute goalkeeper Djordje Petrovic flapped at a corner and Dobbin smashed home to spark wild scenes of celebrations.
A third win in nine days capped a stunning week for Everton, which has nearly wiped out the toughest sporting sanction in Premier League history.
"They've spent a fortune on players, he's (Pochettino) a top manager, but I would say you've got to find ways of winning," said Dyche.
"That's the pleasing thing, we are finding different ways of winning."
