A magical finish from Grant McCann earned three priceless points for the hosts who keep out of the drop zone on goal difference.
But with Wednesday one point above the relegation spots with only a game remaining, their hopes are still good.
"There are several teams still in danger but our destiny is in our own hands and that is what is important," Jones said. "We're not in the position of having to rely on other results.
"Staying in this league will be a far bigger achievement than winning promotion last season to get here."
It was McCann's stunning curling free-kick in the 64th minute that separated the sides, with the visitors struggling to provide any resistance.
"There were a lot of nervous people out there on the pitch and it was always going to take something special to win the game," Jones added.
"We didn't do any better or worse than Peterborough did, but they had that one moment that mattered. It was sloppy on our part to concede the free-kick.
"We decided to play a system that has brought us success away this season, but unfortunately that wasn't the case today. We had a couple of chances but their keeper saved one and we should have done better with another."