With Kilmarnock now the nearest team to the Bairns, Pressley wants his side to maintain their momentum when they host Hibernian tomorrow.
Falkirk came from behind to take a point at both Hamilton and St Johnstone and Pressley wants them to focus on those positives rather than dwell on St Mirren's unexpected points boost.
"The point at St Johnstone was encouraging but the performance was as well," the former Scotland defender said.
"That's two difficult away games and two positive results, which has given us a bit of momentum.
"I said from day one to the players that the one thing we can't concern ourselves with is other results.
"Obviously it's good when other results go your way but the only people that will help us survive are ourselves.
"Nobody else is going to do us any favours, we can't rely on anyone else. It's down to us as team to get the correct results.
"Yes, it maybe didn't go well for us but our full concentration must be the positives we have had in the last week."
One of the positives from McDiarmid Park was the return to the starting line-up of striker Mark Stewart, who has been sidelined by groin issues for much of the campaign.
"I'm delighted to see Mark back," Pressley said.
"I thought, especially in the first half, he gave a terrific account of himself.
"It was his first game for some time. He has suffered due to injuries throughout this campaign, he's been a big miss.
"He gives us something different, we like to counter-attack and at times and he certainly provides us with that added threat with the pace he has.
"After 60 minutes he obviously tired and it was only right we replaced him but overall I was delighted with his contribution."
Source: Team Talk