does that mean to say that every time turbo spools, there is a drop in mileage if so why use turbo engine can use just the DI engines for better fuel economy( Considering only fuel economy not the pick up turbo brings)
That's actually a great piece of doubt sirji.
DI engines are definitely more efficient but they are bad performers. They are not very good at picking up higher loads and have a mediocre mid range, while the turbocharged engines have a ballastic mid range.
Why higher FE?
Simple, because turbocharged engines let you use higher gear ratios as compared to their N/A counterparts.
Example: N/A Indica hardly does 100-105 kph in 3rd gear with engine revving around 4k mark and it takes light years to reach there, while the Indica turbo used to do around 120 kph in third gear at same rpm.
So basically the efficiency of a turbocharged engine is still higher when you take fuel as input and work done as output.
Who is Mr. Turbo Lag then? Well, he is no one but the N/A zone of rev range where the turbocharged engines perform like they are N/A!
*N/A: Naturally Aspirated