''I regret the approach I made to umpire Asad Rauf and realise I shouldn't have behaved in the way I did,'' he said in a statement.
Ponting said he values International Cricket Council's (ICC) 'Spirit of Cricket' campaign and he intends to try and uphold it better in the future.
''International cricket matches are passionate affairs but as the captain of the Australian cricket team, I understand it's my responsibility to uphold the spirit of the game and I know that through my actions last night I let myself and my team down.'' ''This morning I called a team meeting to apologise to the players and to discuss our ongoing support for the 'Spirit of Cricket','' the Aussie skipper said.
Ponting said he would also issue a personal apology to Rauf for his actions.
Ponting was fined his entire match fee after pleading guilty to a charge of breaching Level 1.3 of ICC Code of Conduct relating to 'showing dissent at an umpire's decision by action or verbal abuse'.
He was charged for questioning the wide call by Rauf against Shane Watson in the 33rd over of the West Indies innings and was stripped of his full match fee as this was his second such offence in the past 12 months -- the other being during the second Test against Bangladesh in Chittagong in April -- which automatically raises his offence to Level 2.
All Level 2 breaches carry a penalty of a fine ranging from 50 percent to full amount of the player's match fee and/or one Test match or two ODI ban.