Bale scored a magnificent solo goal and created two others to set up a convincing 3-1 victory for Wales in their international friendly at the Cardiff City Stadium.
The Real Madrid star - the world's most expensive player - looked a class above everyone else on the field as he ran the Iceland defence ragged before being withdrawn after 72 minutes.
Coleman said: "I have just asked him for an autograph!
"He is one of the best I have ever witnessed. He is an unbelievable player, he really is. He is a fantastic weapon for us.
"For the people who came tonight it was worth paying the fee, just for him."
Bale created the opening goal in the 12th minute as he crossed for James Collins to head in from a free-kick.
Iceland replied before the break as a Johann Gudmundsson shot was deflected in off Ashley Williams but Bale was simply too hot for the visitors to handle.
The former Tottenham winger raced down the right and had a shot cleared off the line only for Sam Vokes to head in the second.
Bale then did all the damage himself for the third goal as he charged down the touchline himself, from inside his own half, and cut inside to drill home a low shot.
Describing the third goal, Coleman said: "Iceland are a good team with good defenders, they got to the World Cup play-offs.
"It is not as if he is up against someone who can't play.
"He reminds me of when I was younger, as a 10-year-old playing against 15-year-olds, when he runs round defenders."
After a slow start in Spain following his world-record £85.3million move from Tottenham last summer, Bale has also started to find his feet at the Bernabeu.
He has scored five goals in his last seven appearances for the Spanish giants and Coleman expects at this rate of progress that he will soon be regarded as the world's best.
Coleman said: "He has every chance of winning the Ballon d'Or one day.
"He is playing for one of the biggest clubs in the world. We want to be successful as well and he will have a big hand in that.
"He has a great chance. I'm not sure he thinks about that but, looking around, there are not many others playing like he is.
"I don't want to play it down, he has a great chance if he keeps doing what he is doing.
"How many players have the capacity to do what he does? If he was Spanish or Brazilian people would go crazy, but he comes from a small footballing nation.
"He has to be up there as one of the best players on the planet. You cannot disguise it.
"He was worth the admission on his own."
With Bale capable of such performances, Wales will have hope of pushing for qualification in an expanded Euro 2016.
Bale tweeted: "Always special to be back playing for @FAWales. Good win tonight and important preparation for the Euro qualifiers."
Iceland manager Lars Lagerback admitted his side had been outplayed by Bale, who he already regards as one of the game's best players.
Lagerback said: "He is world class. I don't know if I can find the words to describe the way he is playing.
"He is absolutely in the same bracket as (Lionel) Messi and (Cristiano) Ronaldo."
- Sports & Recreation