Just in case he’s been omitted in error and also looking for some clue that may help you, I’ve checked all pages of the actual roll for the 47th Foot (pdf from National Archives). Unlike some the 47th's roll is almost intact and although a few pages of names of private soldiers are torn ALL pages containing officers are complete. There are quite a number men of 47th who only qualified for the medal without clasps, who must have landed on the Crimea Peninsula but took no part in any actions, he’s not listed anywhere so it would appear Charles Finnerty never actually arrived in the Crimea “war zone” at all.
The 47th Foot went to the Crimea from Malta, via Scutari (on the Bosphorus) and Varna (Bulgaria) and according to the brief regimental history on the web site of the Duke of Lancaster’s Regiment’s Lancashire Infantry Museum, “Cholera had dogged the army ever since Varna”, so I figured it was possible be missed the action through either sickness or being part of some depot detachment; next The Times newspaper.
In the Times of 18 Apr 1854, in the list of Officers as departing Malta on the transport Apollo on the 11th, along with 845 rank and file and six women of the 47th Regiment, he’s named as Ensign Finnerty.
He’s next (that I found) mentioned in an article entitled “Sick & Wounded Fund” by a Times correspondent in Scutari, dated 10 Nov 1854 and published in the Times of 23 Nov 1854. I’ve only skimmed the article and note it mentions the arrival of “Miss Nightingale and 40 nurses”, large hospitals and in particular of interest to yourself his name in this section:
“In the direction of two such extensive establishments much of course depends on the energy with which they are presided over by the medical and military officers in charge, under the superior control of Dr Cumming, Dr M’Gregor has the chief superintendence of the Barrack Hospital, and Dr Menzies of the General Hospital. On all hands they are admitted to be men entirely devoted to their duties. Nor are the services of Major Sillery, the commandant, and of Lieutenant Finnerty, his adjutant and barrack master, less warmly acknowledged. Upon them have devolved very important and onerous functions, which they have diligently and effectively carried out. To their honour be it said, they are both officers who have risen by merit alone from the ranks.”
It appears he spent the whole period at Scutari in that roll arriving back in England on the HM steam transport Resolute mid August 1856 along with Lt Col Sillery commanding the troops on board. At the end of the list of names on the ship, that included Lt Finnerty of 47th, published in the Times of 16 August 1956, it state: “These and the others in the Assistance clear out the establishments ashore lately occupied by the British in the Crimea and the Bosphorus, with the exception of 15 orderlies, under General Storks, at Constantinople.”
In case you are not already aware Charles Finnerty became Ensign from Sergeant Major 25 Oct 1850 and Lieutenant 6 June 1854 as announced in the London Gazette at http://www.gazettes-online.co.uk/