Finney was renowned as one of the game's great wingers and was famed for his double act in England colours with fellow wideman Sir Stanley Matthews.
But playing his entire career at Preston after eschewing the chance for a lucrative move to Palermo, he was denied the silverware his talent deserved.
Armfield said: "He, in my opinion, is one of the really great footballers that this country has produced.
"Even going back to his early days, the Italians tried to snatch him away from England - but he wouldn't leave Preston. He was a loyalist as well.
"As much as anything else, and it's hard to explain to many people today, but it was the way he played and the way he carried himself - his whole demeanour of life. Really, Preston will be a very sad place."
He played in three World Cups in a career which, after being delayed by the Second World War, spanned from 1946-60 and was the first player to win two Footballer of the Year Awards.
Preston North End's players wore shirts bearing his name in their League One match on Saturday afternoon, and Finney's statue has become a shrine to a man born a street away from Deepdale. A minute's silence was held before the game with Leyton Orient.
Bill Shankly, the former Liverpool manager and ex-Preston team-mate, once said: "Tom Finney would have been great in any team, in any match and in any age... even if he had been wearing an overcoat."
Finney was nicknamed the 'Preston Plumber' during his career after his first trade, to which he returned and ran a successful business in after retiring from the game.
Additionally he worked in the media, was chairman of the Preston Health Authority and in 1998 was awarded a knighthood.
Aside from a Second Division championship title, Finney never won any of the game's major honours.
In 1954 the FA Cup final was billed to be his day - a year after his friend and rival Matthews inspired a famous Blackpool win - but Preston were beaten by West Brom.
Preston also finished First Division runner-up twice during his career. They were relegated from the top flight a year after he retired. They have not returned since.
Current club captain Kevin Davies tweeted: "Tonight we have lost a footballing Legend. A true gent and a loyal servant to his beloved PNE. RIP Sir Tom Finney."
Finney remains joint sixth on England's all-time goal-scoring list.
Gary Lineker, the second-highest scorer with 48, tweeted: "Sir Tom Finney has left us. One of the greatest players this country has ever seen, and a true gentleman. #RIP."
Football League Chairman Greg Clarke also added to the tributes, saying: "The Football League is deeply saddened to learn of Sir Tom's death.
"He was quite possibly the finest player to have ever played in the Football League and was a true gentleman. He was also the epitome of the one-club man with few people ever having contributed as much to a single team, their city or our competition.
"He will be greatly missed by the English game."