Goalie hit the ball with his shoe???

NO, the referee's desicion was wrong.
Since the goolkeeper took off one of his shoes during the game, which was an equipment infraction, the referee should have stopped the game at where the ball went out of bound, gave the goalkeeper a yellow card for unsporting conduct and awarded your friend's team an indirect free kick.
Under Law 12 --- Fouls and Misconduct of the Laws of the Game, unsporting behavior is one of the cautionable offenses in which a yellow card should be shown:
“Cautionable Offenses:
A player is cautioned and shown the yellow card if he commits any of the following seven offenses:
1. is guilty of unsporting behavior ... ”

The referee was wrong and he was very wrong.
If it is a goalscoring opportuity, e.g. the ball is rolling towards the goal line, the referee should show the goalie a red card (FIFA Rule 12) and award an indirect free kick (Also Rules 12 and 13) to the attacking side.
If it is not a goal scoring opportunity, then the referee should show the goalie a yellow card (a cautionable offence; FIFA Rule 12) for unsporting behaviour and award an indirect free kick.
I extract the answer from the FIFA when answering a similar question. It explains in details the siutation about players throwing objects to the ball to deny a goal scoring opportunity.
If the object -- hat, dirt, shoe, shinguard, glove, whatever -- remains in the goalkeeper's (or any other player's) hand, it is considered to be an extension of the player's hand. However, once it leaves the player's hand, the object is no longer considered as part of or an extension of the hand. .....Thus, throwing the object and striking the ball is considered to be misconduct. ----FIFA
Rule 12 of the FIFA Laws of the Game
Sending off offences:
A player, substitue or substituted player is sent off and show the red card if he commits any of the following seven offences:

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denies an obvious goalscoring opportunity to an opponent moving towards the player's goal by an offence punishable by a free kick or a penalty kick.
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Rule 14 of the FIFA Laws of the Game

Penalty Kick
A penalty kick is awarded against a team that commits one of the ten offences for which a direct free kick is awarded, inside its own penalty area and while the ball is in play.
and according to Rule 12 of the Laws of the game:
A direct free kick is awarded to the opposing team if a player commits any of the following six offences in a manner considered by the referee to be careless, reckless or using excessive force:

kicks or attempts to kick an opponent
trips or attempts to trip an opponent
jumps at an opponent
charges an opponent
strikes or attempts to strike an opponent
pushes an opponent
A direct free kick is also awarded to the opposing team if a player
commits any of the following four offences:

tackles an opponent to gain possession of the ball, making contact with the opponent before touching the ball
holds an opponent
spits at an opponent
handles the ball deliberately (except for the goalkeeper within his own penalty area).
Obviously, throwing an object at the ball is not a penalty (direct free kick) offence.. . therefore a penalty or DFK cannot be awarded. The correct restart is an indirect free kick from where the keeper threw the boot ...Throwing an object at an opponent however is penalized as a DFK or as a penalty kick.
How long does it take for the goalie to take off his shoe to hit the ball? He would have better spent the time in saving the ball.
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