He is confident the possibility of suspending the division has been “hit on the head” after an email from the Scottish FA asking clubs if they wanted to carry on.
All leagues except the Premiership and Championship were put into hibernation by the SFA on Monday due to rising Covid 19 cases.
Ian Maxwell, the governing body’s chief executive, contacted teams in the second tier on Friday to gauge the appetite for stopping.
Neilson believes they all want to complete the season after agreeing to a truncated 27-game league programme.
“We want the season to continue and the feedback I got is that every other club in the Championship wanted it to continue,” said Neilson.
“I don’t know the reason for sending the email out, but I think it’s been hit on the head now and everybody has decided they want to continue it – which I think is the right thing to do.
“As football coaches and players, we have a responsibility to entertain people just now. A lot of people are sitting in the house, they don’t have the cinema to go to, no shops, no restaurants. They have nothing to do.
“We can provide them with a focal point to watch and talk about and hopefully entertain them. We have a responsibility to keep this league going.”
Every Championship club received a £500,000 grant from the Scottish Government to help ease financial strain caused by the pandemic.
The cash covers the cost of weekly Covid tests for players and staff, which is now mandatory for Scotland’s top two leagues to continue.
“To be fair, the authorities have given us £500,000 each. It’s more than enough for teams to test and see it through,” said Neilson. “It’s now the responsibility of each club, manager and individual player to follow the protocols.
“We’ve spoken to our players about that and they understand it. Every other player should be the same. It’s about playing football and entertaining people.”