Larsson opened the scoring in Sunday's FA Cup third-round tie at London Road with a free-kick which evaded everyone and crept in at the far post and James McClean headed a second.
The Black Cats have now won four and drawn one of their last five games.
"Football is a funny game," Larsson said on ITV. "We seem to be doing things well at the moment and getting a little bit of luck when we need it.
"We want to carry on doing it."
McClean, 22, has impressed by scoring in his last two matches.
"I'm just enjoying my football, the manager's given me a chance," he said.
"I want to do well here."
Sunderland boss O'Neill was pleased with his side's display.
"I thought that in the first half we allowed Peterborough to play in their own half and when they ventured into ours we closed down.
"In the second half we closed down closer to their goal and became more effective."
O'Neill also had words of praise for McClean.
"That's his third game now and he's just been magnificent," he said. "His ability, his willingness to work back and his all-round game you would think he had played 103 games not three games."
