The west Wales region made it six wins out of six in Pool Five to secure a home draw against Munster in the quarter-final, but they were pushed all the way by the gutsy Exiles.
“I am very proud of what we have achieved in this competition so far,” said Davies.
“I was pleased with the win and the fact that we have got a home quarter-final. We were a bit sloppy at times, but you have to give London Irish credit for the way they played, they kept the ball extremely well.
“From my time in the Premiership I knew how good a side they are. To be fair, we had a go in the first half, gave ourselves a platform but could never get away from them.”
Davies added: “Munster in the quarter-finals will be a fantastic day for us. There are a lot of similarities between us. We have a lot of work to do in the league before then, but it should be an exciting occasion for everyone.”
After leading 17-3 at one stage, the Scarlets were forced to endure a spirited fightback from the Exiles, sparked by replacement, Shane Geraghty.
The 20-year-old, a member of England’s Six Nations squad, crossed for a try and kicked a couple of penalties to threaten to upset the runaway Pool Five winners.
However, the Scarlets, who struggled to replicate their recent heroics in Europe, managed to hang on with fly-half, Stephen Jones, landing a late long-range penalty to seal the points and a top seeding for the Welsh region.
With his first touch after coming on for the injured Michael Horak, Geraghty threw out a speculative long pass, only for it to hold up long enough in the wind for wing, Dafydd James, to pluck it out of the air and race 70 yards unopposed.
The try extended James’ lead at the head of the competition’s try-scoring chart, and with Jones again making no mistake with the simple conversion the Scarlets appeared to be in control.
Everitt managed to reduce the arrears just before the break after Irish won a penalty at a scrum in the home 22, but it was taking some desperate last-ditch defence to keep a confident home side at bay.
With 49 minutes on the clock, it was Geraghty who atoned for his earlier error by darting inside the cover for a well-worked try.
The visitors almost took the lead on 65 minutes when number eight, Phil Murphy, drove over only to lose the ball in the process of touching down.
Geraghty duly landed a penalty and, with less than 25 minutes left, they were a point adrift. But with five minutes left, Jones eased home nerves with a penalty from the halfway line.
Irish could have nicked it in injury time when flying wing, Topsy Ojo, almost chased down his own kick, but when replacement lock, Nick Kennedy, was sin-binned for a reckless punch on Simon Easterby, the Scarlets managed to hang on and make it six wins from six in their pool campaign.
Llanelli Scarlets scorers — Tries: Peel, James. Cons: S. Jones 2. Pens: S. Jones 2.
London Irish scorers — Tries: Geraghty. Cons: Geraghty. Pens: Everitt 2, Geraghty.
LLANELLI SCARLETS: Stoddart, James, King, G. Evans, Watkins, S. Jones, Peel, I. Thomas, Rees, Dunlea, A. Jones, MacLeod, Easterby, G. Thomas, Popham.
Replacements: Daniel for G. Evans (80), Manu for Dunlea (59), D. Jones for G. Thomas (59).
LONDON IRISH: Horak, Ojo, Mapusua, Flutey, Bishop, Everitt, Rees, Lea’aetoa, Paice, Skuse, J. Hudson, Roche, McCullen, Magne, P. Murphy.
Replacements: Geraghty for Horak (29), S. Armitage for Everitt (46), Willis for Rees (61), Collins for Lea’aetoa (68), Russell for Paice (48), Fitter for Skuse (61), Kennedy for Roche (55).
Referee: C Berdos (France).