Falcons boss Steve Bates said he expects Wilkinson to be fit to face Leicester next week along with England duo Toby Flood and Jamie Noon, who missed Sunday's game with ankle injuries.
"Jonny got a bang on the head and felt a bit of a stinger down one arm," said Bates.
"He seemed fine at the end of the game, but he was a little bit woozy and the doctor has been having a look at him and we think he'll be fine."
Newcastle may have reached the semi-finals of the European Challenge Cup, but the Falcons have yet to win in the league under Bates, although they are now safe from relegation after Leeds' defeat to Harlequins on Sunday.
"That's some consolation," said Bates, "but it was a pretty poor game today and we were very disappointing in the first half and we looked very tired.
"It's a case of two steps forward and one back. We looked a little bit panicky and not comfortable on the ball and while we may have never been out of it if you looked at the scoreboard that doesn't excuse the level of performance."
Heineken Cup semi-finalists London Irish were also disappointed not to have taken five points from the game.
"We're satisfied with the win but not the performance," said Brian Smith, London Irish's director of rugby.
"It's a long way up to Newcastle and long way down from the quarter-final against Perpignan. We don't have a big squad and we're having to ask people to soldier on and front up.
"We're delighted with the way we're going in the Heineken Cup but we have ambitions in the Premiership to finish in the top six so today was a missed opportunity for us."