I think his question was "why de-rated thrust uses more trip fuel"?
Easy, de-rated thrust will take you longer to climb to your optimal altitude (best SFC). As with a de-rated thrust climb, the a/c has a lower initial rate of ascent and therefore takes longer to reach its transition to its enroute climb profile and then its cruise altitude. Consequently, it spends less time at its optimal cruise altitude and therefore uses more trip fuel.
Bristow p.208