The Clarets finished second in the National League South but lost in extra-time to eventual Promotion Final winners Braintree Town earlier this month.
The manager took over in January 2020 following the departure of Rod Stringer before taking the reins permanently two months later.
Despite the disappointment of last season, Simpson says he will stop at nothing to go one better next season - sticking to his word and signing a new deal.
Simpson said: "Undoubtedly our final game of last season hit everyone incredibly hard, it was really difficult to get over.
"As I mentioned in my post match interview that day, once the dust has settled I was sure that we would look back on the season with great pride and fulfilment.
"I’m certain that we had that but, it has also me even more desire, if I didn’t need anymore it has given me even more to get this club over the line and get them promoted and we have already announced the addition to the training structure.
"We feel like not only as a club will that push us forward but also give us an even better chance on the pitch to get over the line.
"What we have done in terms of the resources and where we finished has been quite incredible and I reflected on that really proudly and really fondly but I am certainly someone who wants to continue each year getting better and better and better.
"Whether we like it or not and whether our resources reflect that or not, the only way for us to improve on the season we have just had is to be promoted and that is what we will be looking to do.
"I am delighted to be remaining at the football club, it has a special place in my heart now and once again.
"I will give it my absolute everything to help this football club get promoted and get it to where it should be."