Northamptonshire’s hopes of a late qualification were ended by a 6 wicket defeat at the hands of Lancashire at Old Trafford.
Further results elsewhere meant even a win for the Steelbacks wouldn’t have proved enough.
A fine opening spell of two for 14 from three overs by Wood, after Livingstone had put the visitors in to bat, had Northamptonshire quickly on the back foot at the start of their innings.
Vasconcelos was brilliantly caught for 12 by wicketkeeper Buttler diving to his left, followed by Emilio Gay who chipped the left arm quick to Luke Wells at mid-on two balls later.
Northamptonshire then suffered a big blow when Willey departed for 10 attempting to hit Liam Livingstone over midwicket to leave the Steelbacks struggling on 47 for three, midway through the seventh over.
Chris Lynn led an initial fightback, launching Livingstone for consecutive sixes in the ninth over but he was then bowled for 35 when Luke Wells had a ball keep low with the visitors on 74 for four, one ball into the eleventh over.
Saif Zaib pulled Mitchell to Wells at fine leg for 12 and the Steelbacks only managed to get any impetus into their innings during a 40-run partnership for the sixth wicket between McManus and Broad.
McManus hoisted a slower ball from Tom Bailey into the hands of Wood at long-on having made 22 while Broad smashed a six over midwicket in his unbeaten 34 off 26 balls.
Wood (three for 17) returned to bowl Tye for 1 as Northamptonshire closed on 138 for seven.
That proved to be below par on a new but slow surface as Lancashire marched into the quarter-finals for the sixteenth time in 20 seasons.
Northamptonshire struck two early blows as the hosts set off in pursuit of their target, Jos Buttler skying a short ball from David Willey to Saif Zaib on the cover boundary for 11. Steven Croft swiftly followed after top edging Tom Taylor to AJ Tye for 5.
That left the Lightning ending the powerplay on 43 for two but Salt picked up the scoring with a six off Freddie Heldreich during a 35-run partnership in five overs with Liam Livingstone.
Livingstone, the stand-in Lightning skipper, went for 11 slicing Taylor to Ricardo Vasconcelos at gully as Lancashire reached halfway on 74 for three but Daryl Mitchell was quickly into his stride driving Taylor for six into the pavilion seats.
Salt continued to score freely as the hosts reduced their target to a-run-a-ball 44 before a mix-up saw Mitchell run out for 17.
Undeterred, Salt reached a 40-ball half century by lifting AJ Tye for six over long-on, and then took four, six, four off Justin Broad in the fifteenth over as the Lightning raced towards their target.
The opening bat ended the contest in style with six off Taylor in the seventeenth over to finish unbeaten on a Lancashire-best 74 alongside Dane Vilas (10 not out).