The incident occurred in the 23rd minute when the North End midfielder made what looked an innocuous challenge on George Boyd.
While Boyd eventually got up, Nicholson rolled round in agony for some time before being stretchered off with a leg brace on.
Irvine said: "He has broken his leg which is bad news but it isn't displaced which is probably good news.
"But he is obviously going to be out for a considerable amount of time now.
"It was his lower leg and it will be months before he's back but the fact it's not displaced will help the process of healing, but we don't really know how long it will be."
Nicholson was booked by referee David Webb as he was stretchered from the field of play in the 23rd minute.
Asked whether he felt a booking was necessary, Irvine added: "I didn't expect it to be that serious an injury, I just expected it to be a clash of shins and I thought everyone would be okay after limping about for a bit.
"I didn't anticipate anyone being injured and I was very surprised by the yellow card.
"I thought it was a bad decision. But it was fairly clear when you've got that great big air cast thing on and your being stretchered off in agony. It seemed a poor decision."
Two well-crafted goals, the first scored by Neil Mellor and the second by Billy Jones, saw the Lilywhites triumph.
Of his side's victory, which sees them climb to third and remain unbeaten, he added: "I'm really pleased to get another victory and I'm absolutely delighted to get another clean sheet.
"I thought there were periods when we played really well especially in the first half.
"I was more pleased with the way we created opportunities."
Peterborough boss Darren Ferguson, whose side are still searching for their first win the Championship, felt his side's lack of concentration at the back cost them dearly.
He said: "It's something I spoke about before the game, concentration especially at the start of the game. "They got an early goal in the eighth or ninth minute and it's hard enough at Preston away.
"And then obviously it goes to two and we get back at them a little bit and get in behind them but we couldn't really break them down especially after they went to five in midfield."