Thompson took charge of the Seasiders in the wake of Ian Holloway's departure for Crystal Palace, a move that was confirmed less than four hours before kick-off at Pride Park.
The club's troubled week showed on the pitch with a disjointed performance and Thompson hopes he will still be considered for the role despite a bad first day at the office.
"It came as a bad blow after a very difficult week and you could see in that performance how much it took out of the side," Thompson said.
"But I would not like to think that any decision on my future will be based solely on what happened in one match.
"I'd like to think that the things the club has achieved in this period will be remembered because I believe I have played an important part.
"It is all up to the chairman but I will get another chance to show my credentials when we play away to Sheffield Wednesday on Tuesday.
"The team that plays there will be the one I pick and I would expect the hard words and home truths spoken in our dressing room after this performance to have the desired effect.
"I won't be going there (to Palace). Ollie has taken Keith Millen with him and my only priority is making sure we are in the right frame of mind to give a true picture of our quality against Wednesday.
"It is not long ago that these players were getting rave reviews. They are the same players but we need to sort a few things out defensively to start moving back in the right direction again."