"It felt at the time like I had taken a hit, but I am told from people on the sidelines that it wasn't, it just felt like that because of the pain.
"Now I have to focus on getting past this, and I am determined to put it behind me and come back even stronger.
"I have recovered from injuries before, and I am totally focused on moving onwards from here."
Wilkinson sustained the injury in the second half of the Falcons' Heineken Cup defeat in Perpignan, and was taken straight from the Stade Aime Giral to a local clinic for scans.
Newcastle Falcons club doctor Andy Ramshaw said: "We must be thankful at least that the injury is not as serious as it could have been, and that the anterior cruciate ligament was not damaged.
"From the initial scan results we have, a recovery period of four to six weeks looks likely, but we hope to know more this week after seeking specialist advice.
"I would also like to personally thank the Perpignan club doctor, Olivier Lambert, for going to enormous lengths in calling people in at very short notice and making it possible for us to get the scan done so quickly after the match."
Director of rugby, Rob Andrew, said: "It's obviously devastating news that again we will be without Jonny, and he was in the best shape of his life, but the injury could have been a lot worse and I am sure he will bounce back.
"Jonny has showed tremendous strength of character in coming back from injury in the past, and he is equally determined this time not to let it get the better of him."
The Falcons have a severe shortage of fly half options ahead of Sunday's crucial Heineken Cup tie at home to Newport Gwent Dragons, with Dave Walder also out with knee cartilage problems, as well as development team fly half Toby Flood, who is sidelined with a hand injury.
Andrew said: "We're having desperately bad luck with injury to fly halves at the moment, but we will take a look this week, see where we are and formulate a plan from there."
In other injury news, centre Jamie Noon will be tested this week after leaving the field of play with a bang to the head. A decision will be made in the week about whether or not he is fit to play on Sunday, but at this stage he has not been ruled out.
Second row Andy Buist, who was also taken off injured in the second half on Saturday, has sustained a knock to the knee. No ligament damage has been detected, and club medical staff will examine him further in the week.