Connacht edged victory by 14 points to 12 in front of a packed Stradey Park to consign the Scarlets to their first defeat of the season.
"We lost a close encounter against a very competitive team," he said, adding:
"We came out the wrong end of a tight game."
Connacht, highly unfancied by many before the match were able to defeat Llanelli in their own backyard thanks to an expert tactical performance, and a large slice of luck.
Intense Scarlet forwards pressure yielded two penalty kicks at goal as the clock ran down, but kicker Gareth Bowen was unable to convert, leaving the home fans distraught.
Jenkins was thoughtful in his post match assessment of Bowen's two missed penalty kicks at goal, errors that ultimately cost his side dear.
"We have not taken an opportunity which I think we genuinely could have had. To have an involvement in all competitions is what this region wanted, said Jenkins.
"We have lost a game we could have won and had chance to win. We have gifted Connacht a semi-final place."
Despite his obvious disappointment, Jenkins added, "I have told the young boys there is nothing to be ashamed of."
Llanelli return to Celtic League action this weekend with a visit to Edinburgh on Friday night.