Having lost four times to Toulouse in the last two years, tries by Scott MacLeod and captain Simon Easterby saw the Scarlets home, but Davies expects a tough time in Saturday's return leg.
"I am over the moon," he said. "We started very well and although we gifted them two tries, the boys showed a great deal patience and tenacity. The boys showed dogged determination to charge down those last two kicks.
"We have now won three out of three and I couldn't have asked for more at the start of the season. Toulouse will take heart from a brave performance and I expect it will be a tough day at the office on Saturday."