After victory for the Birmingham Bears earlier, the Rapids had to win to deny their Midlands rivals the final qualifying position but their 169 for six proved insufficient as Inglis made them pay for a dropped catch on 14 by hitting eight sixes and 10 fours in his career-best unbeaten 118 off 61 balls to see the Foxes home with 13 balls to spare.
Ed Barnard had hit 43 from 24 balls to top score for the Rapids, Jake Libby making 35 and Ross Whitely 31 but no-one could go on to make the big innings that was needed.
Worcestershire first-team coach Alex Gidman said: “It’s been a tough but really enjoyable campaign for us so I’m disappointed for the players and supporters that we couldn’t get over the line and get into that quarter-final.
“We thought we batted really well to get back into it and put up a competitive score that was about par, but that was an exceptional innings from Inglis and this is the beauty of the game that one guy can bat magnificently like that and win the game single-handedly.
“We’ve had a few like that against us this year from some amazing cricketers and we have to learn to emulate performances of that kind. It would have been nice not to have been on the receiving end tonight but fair play to him he played very, very well.”
Earlier, the Bears closed their group campaign with a 14-run victory over Northamptonshire Steelbacks.
The Bears’ total of 191 for five owed much to a dazzling debut from Chris Benjamin. The 22-year-old struck an unbeaten 60 (34 balls, seven fours, two sixes) to lead a recovery from 68 for four.
The Steelbacks, qualification hopes long extinct, mustered 177 for eight in reply. They threatened briefly through Ricardo Vasconcelos (39, 33 balls) and Josh Cobb (35, 18 balls) and Rob Keogh bashed an unbeaten 55 (33 balls) when the cause was lost, but the chase fell away in the face of pressure built by superb spin bowling – 4-0-20-2 – from Jake Lintott.
Bears batsman Chris Benjamin said: “It was a very special day for myself. To be out there and experience that atmosphere from the crowd. I am just delighted that I could get a score to contribute for the team.”