does index of my data which is of type "Date time index" plays a part in reggression?
You can take the date into account, but you should convert it into numeric value.
Suggestions:
1) Consider "datetime" package in python to change it to numeric, or some other techniques such as indexing with date-time, and converting the index value to numeric, float, etc. I don't have your exact case, so cannot say specifically. 
or
2) If you have time series data, then in many cases ARMAX, ARIMAX, Seasonal ARIMAX models can do a really good job.