Director of cricket Giles White says it is important Hampshire forget their T20 Finals Day disappointment quickly.
Lancashire beat Hampshire by 41 runs and go through to face Birmingham Bears in the T20 Blast final at Edgbaston.
Birmingham Bears, Hampshire, Lancashire and Surrey will chase the season's first trophy at Edgbaston on Saturday.
Adil Rashid's 5-33 helps Yorkshire finish top of Group A with a six-wicket win at Hampshire in the One-Day Cup.
Hampshire T20 captain James Vince hopes glory at Finals Day on Saturday can be the start of a double celebration.
Hampshire re-sign leg-spinner Imran Tahir subject to visa clearance for final two County Championship matches.
Hampshire continue their push for promotion from Division Two with a 196-run victory over Kent at St Lawrence.
Michael Carberry, Jimmy Adams and Will Smith set up Hampshire's declaration 501 runs ahead, before Kent close on 94-2.
Kent suffer a poor second day as paceman Chris Wood (5-39) leads the charge for Hampshire by taking five wickets.
An unbeaten 75 from Sean Ervine puts Hampshire in control against Kent on day one at the Spitfire Ground.
Hampshire all-rounder Chris Wood signs a one-year contract extension at the club which takes him through until the end of the 2016 season.
Hampshire collapse to a five-run defeat as Essex book their place in the quarter-finals of the One-Day Cup.
Hampshire and Worcestershire take a point each from their abandoned One-Day Cup group A match at the Rose Bowl.
Muhammad Azharullah takes 5-38 as Northants bowl out Hampshire for 249 before rain ends their One-Day Cup tie as a no result.
Niall O'Brien's 105 steers Leicestershire to a six-wicket win in a rain-affected One-Day Cup game at Hampshire.
Hampshire captain James Vince said he was proud to help fire the county to their fifth successive finals day.
James Vince's unbeaten 93 leads Hampshire to victory over Nottinghamshire to secure a place at T20 Blast finals day.
Spinner Jack Taylor takes 4-38 as Gloucestershire recover from a poor batting display to beat Hampshire in the One-Day Cup.
Australia all-rounder Glenn Maxwell says he hopes to return to Hampshire next year as an overseas player.
Glenn Maxwell hits 146, his highest one-day score, as Hampshire beat Lancashire by 148 runs in the One-Day Cup.
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