Niall O'Connor kicked the winning penalty for Connacht after Mark McCrea's try had brought the hosts back into the match from 11-3 down.
The Scarlets were close to a second win of the season following Aaron Shingler's try at the start of the second half but had to settle for a losing bonus point after the Connacht fightback.
"We manned-up well and showed physical presence but we also will be hard on ourselves this week on some of our decision-making", said Davies.
"We were competitive for the lion's share of that game and in the first block there was not much in it.
"But we need to be sharper about some of the choices we make and that's about experience.
"We held onto the intensity of our game throughout once again and that is something that has been a positive for us throughout the pre-season fixtures and now in our first two league games.
"It was a real battle in the conditions, there is plenty for us to focus on this week before we go out to Munster and some things that we'll put right."
After two penalties from Dan Newton, Shingler extended the Scarlets lead, taking the ball from Iestyn Thomas and going over in the left corner.
The hosts finally responded after a stuttering first-half performance and Henry Fa'afili wrong-footed the Scarlets defence to put in McCrea, with Matthew Jarvis converting, before his replacement O'Connor scored the decisive penalty ten minutes from time.
Connacht head coach Eric Elwood also admitted it was a far from polished performance from this troops.
"The two good occasions we got into their 22 in the first half," said Elwood. "We threw the last pass away, so maybe we lacked a little composure in some areas."
"But we got ourselves back into the game and a foothold at scrumtime.
"Henry showed some great footwork and with Mark running a great line off his shoulder it was a well taken try.
"We ground it out, we squeezed it out and thankfully we were able to guide it home."
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