His introduction to the union code - delayed by more than a year because of injury problems - has proved slow and unspectacular.
But Gaffney remains upbeat about the ex-Wigan star's prospects, despite a low-key full debut in Saracens' 36-24 EDF Energy Cup defeat against London Irish.
"He is still a way off and he has some learning to do, but he will get better the more games he plays," said Gaffney.
"His desire is still to learn, and I don't think it will be long before we see a dramatic change. It is part of the learning curve at present."
And Gaffney believes blindside flanker is the role most suited to Farrell, despite many experienced judges claiming he might make more of an impact at inside centre.
"I still think his best position is at six," added Gaffney.
"Everyone is suggesting he plays 12, but the running lines Andy has at the present time - he has a trait where he runs across field - is probably the worst trait a 12 can have.
"Consequently, with some of the things we are trying to correct, it wouldn't be a positive as far as the 12 is concerned.
"They (the Rugby Football Union) originally acquired Andy as a 12, but (England head coach) Andy Robinson has changed his mind and at the moment he is happy to go down the route of six.
"He knows a lot of the areas where he has to improve, but some of the things he is doing now are fine.
"He can step into first receiver and has the ability to transfer the ball and kick well off his left foot. Those are things he can still do at six. We are trying to break the traditional six mould."
Farrell has featured in two Guinness A League games, an Anglo-Welsh clash and had 16 minutes as a Premiership substitute this term.