Griffiths is the top scorer in the SPL this term with 13 and Fallon believes the on-loan Wolves striker's goals are the main reason for Hibs' lofty position.
"I think they're doing well, but when they came here I thought they struggled," he said of Aberdeen's 2-1 win at Pittodrie in September.
"I feel their strikers are dragging their team along. Griffiths, if we stop him, they won't score.
"He's the one getting all the goals. I believe that we're a better team than them. Obviously we'll have to prove that on the day tomorrow."
Victory at Easter Road, where Hibs are unbeaten this term, would take the Dons to second in the SPL, separated from their hosts by goal difference, but Fallon's sights are set even higher as his side aim to respond from the 2-0 loss to leaders Celtic.
"Some people are happy for Celtic to go off and win it, but I'm one of those guys that believes we can win it," the New Zealand forward said.
"If people believe Celtic are going to win it, they're going to win it.
"If we don't believe we can do well and push up higher, then what's the point of even playing?
"I really don't see the point in people just giving Celtic the title already.
"That's not how I work. I work through belief and having faith.
"Celtic have probably got the biggest squad, but we've got the strongest squad after them." Craig Brown praised Fallon for his "infectious enthusiasm" but prefers a different approach publicly.
"Under-play your hand is the way to do it," Brown said.
"I'm not going to publicly say what we're going to do to Hibs, beat them and finish above them - all that does is motivate them.
"All that does is give Pat Fenlon his team talk: 'listen to what he's saying'.
"Everyone acknowledges Griffiths is the leading scorer in this league, he scores freely, all kind of goals.
"There's no doubting that Griffiths is the man that has been influential in getting Hibs to where they are.
"Griffiths is their version of Niall McGinn. McGinn missed five games this season, so you don't know what tally he might have had."
McGinn has netted eight times this season and is likely to continue up front on Saturday. Fallon made his first appearance since August against Celtic last weekend after a problematic stomach injury was finally resolved by treatment from a specialist. The 30-year-old said:
"I've had this since the World Cup. No-one knew what is was.
"I tore my abdominal muscles and they healed back and got a grip of my nerve.
"I'm glad to be getting rid of it. I'm just happy to be back."