Thomas is in a comfortable condition in hospital having undergone heart surgery after being taken ill at training on Thursday.
Members of the Scarlets management have been to visit the Wales international as he recovers, and Davies told of how the 29-year-old wanted to wish his team-mates the best before they went on to claim a win that sees them close in on a first LV= Cup semi-final place since the inaugural Anglo-Welsh tournament during the 2005-06 season.
Davies, whose side were shorn of 11 internationals preparing for RBS 6 Nations duty, said: "It's been a tough few days.
"I went to see Rhys before the game and he is not great, he is recovering but he did say to wish the boys all the best, and I passed that on to the boys, and they certainly delivered for him."
A brace of tries from Tongan winger Vili Iongi and a score from replacement prop Deacon Manu, plus three conversions and two penalties from full-back Dan Newton secured a win that means a repeat performance at Sale next week will seal a last-four spot.
The result was made all the more impressive by the strength of a London Irish starting XV that included the majority of their first-choice selection.
Young back-rowers Matt Gilbert and Kieran Murphy shone for the hosts, while centre Adam Warren and Newton were composed behind the scrum.
And Davies felt the display ranked as the best squad performance of his tenure.
"This game and last week's win in Castres have been fantastic squad efforts and show the depth we have and how that's building," he said.
"That was as strong a team as Irish could put out and we showed a lot of resilience and spirit, and when opportunities came we took them.
"That was the best squad performance that we have been able to put out, going back maybe to even a long time before I was here."
Irish's points on Saturday came courtesy of Topsy Ojo's second-half try and four penalties and a conversion from full-back Tom Homer, but the Exiles paid the price for a failure to take their chances as they extended their miserable record of never having beaten the Scarlets.
Twice in the opening quarter they were denied tries by the video referee, as Homer and wing Marland Yarde failed to ground the ball over the line, before lock Bryn Evans and flanker David Sisi butchered an overlap towards the end of the first half.
Coach Toby Booth said: "That was frustrating, we had the ball for long periods in the right areas, we had two TMO decisions go against us, not that I'm saying they were the wrong decisions, but shows we have been in good positions and that proved the difference.
"You have to convert when you get there and we were probably guilty of not doing that."
The game also proved a miserable return to his former club for Exiles centre Steven Shingler, just weeks after a furore erupted over his international eligibility, as he was forced off after taking a knock in the first half.
The 20-year-old's previous visit to Wales had resulted in a sending off against Cardiff Blues in the Heineken Cup.
Shingler had been named in Scotland's RBS 6 Nations squad but the International Rugby Board had advised that he is only eligible to represent Wales having played for their Under-20s.
The Scottish Rugby Union had stated they would ask the IRB's Regulations Committee to formerly consider the matter, but Booth said Irish were not aware of any further developments in the matter.
"There is no situation. The IRB have ruled that way and until someone lodges an appeal then that's it.
"We just want to support him. This has never been about Scotland or Wales but about a young man with an opportunity to play international rugby.
"If he were to play for Wales he would be very proud to do so if the chance ever comes along.
"All we spoke about was making sure he has a decent opportunity at some point to play international rugby as we believe he has the ability to do so."
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