The Foxes posted a huge 214 for six in their 20 overs, with Cobb declaring that total was '15 or 20 over par'.
The Steelbacks still very nearly chased that target down though, but Jimmy Neesham's run out in the final over proved crucial as Northants closed on 213 for seven.
It was the fourth straight defeat for John Sadler's side, who have now completed their North Group campaign, and means the Steelbacks cannot qualify for the last eight.
It was a feisty evening in Leicester, and there was some animosity heading Neesham's way as he was run out in the final over with the game very much in the balance.
Steelbacks skipper Josh Cobb, one of three Steelbacks players to hit a 50 alongside Chris Lynn and Neesham, felt that was unnecessary, but accepted that emotions can get the better of players in high pressure situations.
“It was a close game and there were some heated moments at the end when Jimmy (Neesham) got a couple of send-offs, which is not necessarily the way you want to see the game played," said Cobb, a former Leicestershire captain.
"When it is a close game and there is a lot on the line these things can happen.
“It was a great game, which would have been better still had we been on the winning side.
“Their total of 214 was clearly chaseable, but they were probably 15 or 20 over par.
"We weren’t quite on it with the ball or in the field, which has been the case for the last week, which hasn’t been good enough.
"If we’d had one more good over that had gone for six or seven then we might have got over the line."
Aussie import Lynn went past 500 runs for the tournament during his innings of 68 from 37 balls, and Cobb paid tribute to a player who has enjoyed a fantastic spell in Steelbacks colours.
“Chris Lynn was great again," said Cobb, who scored 53 from 40 balls.
"He has had an outstanding season and it’s obviously good to be batting with someone who can clear the ropes at will.
"We kept it at 12s for a lot of the time and if we could have had one more big over we would have been close to getting over the line but it was not to be.”
The Steelbacks are out of the Blast, but on Sunday they host India in a T20 friendly at a sold out County Ground.