The 22-year-old winger, who is on a season long loan deal at Blues, was jailed for three months on a drink-driving charge at Aylesbury Magistrates Court last week.
His lawyers had planned to appeal the sentence but have now dropped those plans and Pennant will see out his sentence which he his serving at Woodhill Prison in Milton Keynes.
Blues boss Steve Bruce has revealed that upon his release from jail he will still be trying to turn Pennants loan deal into a permanent move.