Jefferies said: "I think we deserved our victory. We've maybe now come through a wee patch when we weren't at our best.
"We're now looking forward to Tuesday, but this result will have no bearing.
"It's a one-off, on the night, but if we play as well as we did we'll have a good chance.
"Records are there to be broken so we don't pay too much attention to having a hold over them. We give them every respect because they are a good side, their results show that.
"They have lost Stokes who is a hard man to replace, and maybe a wee bit of the speculation might be affecting Alan Gow."
Jefferies saw his side profit from a first-half error by Falkirk new-boy Dean Holden, who carelessly gave the ball away to Naismith ahead of the opening goal.
He added: "He has given the ball away crazily in the middle of the park, but we still had a lot to do.
"It was a fantastically weighted pass from Naismith and Nish has stuck it away brilliantly.
"It was a mistake and we cashed in on it, but you have to give credit to the pair of them."