Jackson produced a number of costly misses against the defending Premier League champions and was eventually substituted off in the 67th minute for 18-year-old Marc Guiu.
Mikel took aim at Jackson's ball-striking technique in a scathing takedown.
'You need to have a striker who knows how to hit a ball in the back of the net and that's what we don't have,' Mikel told beIN Sports.
'I know I talk so much about him and sometimes I sound like I disrespect him, but I don't disrespect him.'
Nicolas Jackson wasted a number of good opportunities in front of goal for Chelsea