Jut over 2800 fans, with a small travelling contingent from the Blue Toon, were in attendance as the Bairns ran out 2-1 winners at the Falkirk Stadium.
Craig McGuffie put the hosts 1-0 up on 14 minutes and Paul Dixon made it 2-0 after the break.
Substitute Jordon Brown scored a consolation for the visitors with almost the last kick off the ball but the outlook of the game could have been so much different had Peterhead not been denied what looked a stonewall penalty inside the opening two minutes as Leon McCann brought down Josh Mulligan.
“Decisions change games,” said Nicholls.
"A stonewall penalty in the first minute and the referee is easily influenced by the crowd and decided not to give it.
"We didn't create a lot but we created a few wee half chances and got the goal and potentially should have had another penalty – the referee’s not seen that, I don't know what game he's watching to be fair.
"Our boys battled away, at 2-0 down they could have thrown the towel in but they didn’t, they kept working away and got the goal and it's just a shame that time ran out for us.”
Nicholls also praised the young look Blue Toon outfit who battled well against their full time opponents and handled the pressure from the near 3000 home fans well.
He said: "The younger ones that have come in and have shown a real good appetite and a certain maturity.
"It’s about keeping that going and getting a bit of confidence in them.
"I thought our boys gave everything and looked as fit as them come the end of the game.
"Falkirk always have a really vociferous crowd that cheer the players on and I think our boys did really well coping with that.
"They seemed to relish that in the second half because we created a couple of good chances.”
Nicholls also praised goalscorer Jordon Brown as he continues to build back to full fitness.
"Goals like that will give him a lift, you can count on him for maybe seven to ten goals a season and we're hoping he can do that again.”