An under-strength Chelsea side never looked like pulling off the incredible comeback it would have taken to reach the Champions League quarter-finals.
Tammy Abraham scored their goal in an otherwise largely one-sided second leg as they were again well beaten by a classy Bayern Munich side.
The Blues, 3-0 down from the first leg, always faced a tough task in Munich.
And it became even tougher when Robert Lewandowski tucked away a ninth-minute penalty after being brought down by keeper Willy Caballero.
After Mateo Kovacic had given the ball away, Ivan Perisic slotted home Bayern’s second goal on the night.
Callum Hudson-Odoi seemed to have pulled a goal back with a fine right-footed strike.
However, after a VAR check the goal was disallowed because Abraham had been in an offside position.
Abraham did pull a goal back a minute before half-time by tapping in after Emerson’s ball across the face of goal was spilled by keeper Manuel Neuer.
Chelsea boss Frank Lampard will look to stamp out the kind of defensive shortcomings which have been evident all season.
They were evident again when Lewandowski found space on the left and crossed for an unchallenged Tolisso to score from close range.
And Lewandowski rounded off Bayern’s emphatic victory with his second goal of the night – a fine header from Alvaro Odriozola’s right-wing cross.
Chelsea: Caballero, James, Zouma, Christensen, Kante, Kovacic, Barkley, Hudson-Odoi, Mount, Abraham (Giroud 81).