George Garton, batting at No7, was top scorer with 41 as the Sharks lost wickets regularly to lose by 21 runs.
Wright said: "We're obviously disappointed but credit to Kent - they played really well. DBD (Daniel Bell-Drummond) up top played outstandingly.
"He got that big score and we didn't have anyone who went on and got that big score. Then Stevo - old man Stevo! (Darren Stevens) - finished it off nicely for them and got them a decent total. It was probably always going to be just above par.
"We still felt if we got a platform we could chase it down but we lost early wickets and that made it difficult."
Asked on Sky Sports whether the Sharks were one batter light because of their strong bowling unit, Wright said: "It is what it is. We've been like all the way through the tournament and we've played really well. It's always for the top four or five to get a big score and we haven't done that today and that's the big difference.
"I thought we dragged it back really well. At one point they looked on for 180 or 200 so to do that was a good effort but it was not enough."
This was a Sharks swansong for Phil Salt and Chris Jordan - now off to Lancashire and Surrey respectively - and Wright acknowledged it was sad to see them go but said: "It's up to those of us at the top of the club to try to replace them the best they can.
Match report by Aadam Patel
DanielBell-Drummond’s finely crafted 82 spearheaded Kent Spitfires to a first Vitality Blast final since 2008 with a 21 run victory over Sussex Sharks.
Bell-Drummond struck his sixth half-century of the competition - two more than anyone else - and was accompanied by an unbeaten 47 from 45-year-old Darren Stevens which helped the Spitfires to set a challenging target of 169 for the Sharks.
A fantastic bowling performance, led by Fred Klaasen’s four-for, ensured that it would be Kent and not Sussex who would go on to face Somerset in the final.
Having chosen to bat, Kent lost Zak Crawley and Joe Denly to George Garton in the Powerplay, but quickly got out the blocks - including taking Tymal Mills for 18 off one over.
Bell-Drummond held the innings together with a superb knock which included seven fours and two sixes - one dispatching Mills over his head and the other smearing over midwicket - and brought up his half century in just 29 balls.
Across the 11th and 12th overs, Kent lost three wickets for one run in the space of five balls to slip from 93 for two to 94 for five.
First, skipper Sam Billings also lost his leg stump to Ravi Bopara before Jack Leaning was clean bowled for a duck by Mills before Jordan Cox poked behind next ball.
Stevens left the hat-trick ball before accelerating the Spitfires with seven boundaries - although Bell-Drummond heaved to cow corner, Grant Stewart edged behind and Qais Ahmed was run out. Mills the pick of the bowlers with three for 33.
The Sharks never really looked threatening, losing wickets at regular intervals throughout their run chase.
Phil Salt edged behind off Fred Klaasen before Luke Wright dragged one on off the bowling of Matt Milnes. A stunning grab by Jack Leaning sprinting in from deep cover meant the end for Delray Rawlins and left Sussex with just 40 for three at the end of the Powerplay.
The Darren Stevens show continued as he got David Wiese to drag on with his first ball and just as Ravi Bopara was starting to look settled, he was bamboozled by a beauty of a delivery from Qais Ahmad to leave the Sharks reeling at 57 for five.
George Garton threatened to winch open the game again with an explosive 23-ball 41 before he was caught at third man.
But Harrison Ward was caught, Tymal Mills castled by Matt Milnes, while Klaassen returned four for 17 when he rounded off the rout with the wickets of Chris Jordan and Archie Lenham.
Kent went on to beat Somerset in the final.