After a dramatic 14-run victory at Trent Bridge last week, Cook will lead his side out against Australia at Lord's on Thursday looking to take a firm grasp on the famous urn.
England have been loathe to chop and change too much under team director Andy Flower, particularly after a win, but Finn was noticeably short of his best in Nottingham.
He started well, narrowly missing a hat-trick in the first innings, but tailed off somewhat after that initial burst.
He was not required by Cook until 30 overs of Australia's second innings had passed and on the tense final day chase, he was targeted by Brad Haddin and swiftly pulled from the attack.
Tim Bresnan is standing by, and offers superior batting, while Durham's Graham Onions also takes his place in the 13-man squad and is arguably England's most accurate seamer.
Cook would not lift the lid on England's thinking, but admitted the final make-up of the bowling attack posed a difficult issue.
"Obviously you try and be as loyal as you can to your players when you've won a Test match," said Cook.
"You want players confident they're going to get a good run. But on the other hand you always pick a side you think can win the Test and you do have to make tough decisions.
"I'd love to say the guys who play under me feel they've got my backing but you do have to take tough decisions for the good of the side.
"You need to look at the best balanced attack in the conditions available. We all know you need 20 wickets to win a Test match. Sometimes there are different ways of going about that.
"Part of the skill of being a selector or to weigh up all those conundrums and try to get right answers in the end."
If that all begins to sound a touch ominous for Finn, then he can rest assured that the Lord's' factor will also come into England's considerations.
Middlesex man Finn has a fine record on his home ground, taking 29 wickets at 20.65 in five Tests - comparing with a career average of 29.40.
"Your record at a certain place can play a part," conceded Cook.
"You always try to find the balance of the attack for the conditions you find; past form and past bowling (at a venue) is very important."
Cook had no fitness worries to report, with James Anderson ready for action after taking on a hefty workload to grab 10 wickets in the match and no cover necessary for wicketkeeper Matt Prior following a mild Achilles concern.