The construction 'Not only ...but also' is a fixed phrase, so you do need the 'also'. But note the word order. Your sentence should be either 'The car is not only economical but also feels good to drive.' (standard word order) or 'Not only is the car economical, but it also feels good to drive.' (inverted word order following 'not only')

"Not only" is always followed by "but also."

The car is not only economical but( aslo) good for driving.