He was replaced by Warren Fury and Smith is confident Hodgson will meet up with Ashton's squad.
"Paul took a blow to his leg and it tightened up a little bit but he'll be fine to front up with England on Monday - there's no problem there," Smith said.
"The fact that Mike Bundy, our club doctor, also works for the RFU (Rugby Football Union) meant he was quite anxious to get him off.
"From our perspective, we want to look after him because he's got international aspirations and Warren Fury is a very talented scrum-half as well.
"When one bloke steps aside, we expected another one to step up and that gave Warren a chance to do that."
The Exiles had not won on the road in the Premiership since March 10 last season but two tries in four minutes midway through the first half laid the platform for their bonus-point success.
Outside centre Delon Armitage bundled his way over in the left corner on 17 minutes before Argentinian wing Tomas De Vedia finished off a scintillating move which cut Leeds apart moments later.
Those scores put Irish in total control and although Leeds battled game throughout, and came back into contention with a 45th-minute try from full-back Leigh Hinton, Irish claimed their third score through Samoan winger Sailosi Tagicakibau.
Yet Leeds were still not done and wing Tom Biggs crashed over with 10 minutes remaining for a converted try which tied the scores at 21-21.
However, Irish replacement David Paice quickly claimed his side's fourth try to edge the visitors back in front and finally lay their travel sickness to rest.