The Reds claimed just their third clean sheet in 20 Championship outings and are still eight points from safety.
Peterborough have the worst defensive record in the division, with Saturday’s stalemate also their third clean sheet of the season.
Barnsley were unable to find a way past the home defence but Andersen is confident the Tykes will improve on that front moving forward.
“There were a couple of chances for both teams, but I think we were most of the time well organised,” reflected Andersen.
“We could have been a bit better on the counter-attack, but we will work on this next week and I believe we will improve.”
He continued: “We are obviously happy for the clean sheet – that’s important, also, to win games.
“So, we’re happy about that and just have to keep that confidence we get from clean sheets and take it into the next game.”
Barnsley were backed by 1,200 supporters in Peterborough.
Fans on all sides of the ground were forced to stay in their seats towards the end of the game when a floodlight failure stopped the contest with around 80 minutes played.
Andersen was grateful for the support as the Reds ended their three-game losing streak.
“It was great support,” he added.
“You could hear them all the time, cheering, so thank you so much for the support – it was great to have them.”
Barnsley return to Oakwell this weekend as they prepare to welcome Huddersfield Town to South Yorkshire.