Spain's win makes them the first team to win two consecutive European Championships with a World Cup sandwiched in between and Prandelli said they deserve all the plaudits they will get for that achievement.
"They made history and deservedly - they have a lot of players who are tried and tested at this level and even though they don't play with a classic striker they certainly cause you plenty of problems," said the Italy coach who said his team had simply struggled for fitness.
"We played against them in the group stage and I thought we were excellent in that first game because we were 100 percent fit," he said of the 1-1 draw three weeks ago.
"Against a team like Spain I think you really need to be good in tackle and above all fit, they totally dominated this evening and we have to congratulate a great side for their victory."
Italy beat Germany on Thursday in their semi-final while Spain had extra time to recover from their penalty shootout victory over Portugal the previous day.
"I think we have had a terrific European championships, the only regret is that we didn't have a few more days to rest up before this game," added Prandelli.
Italy lost left-back Giorgio Chiellini in the 21st minute, just seven minutes after falling behind to David Silva's opener.
Then, after switching Antonio Cassano for Antonio Di Natale at the interval, and seeing Di Natale have two chances, Prandelli took out midfielder Riccardo Montolivo for Thiago Motta.
Motta lasted just four minutes before he was carried off the pitch on a stretcher leaving the Azzurri down to 10 men for the final half-hour.
"We came up against a terrific side, they are world champions, but when you are down to 10 men, you can't carry on, the game is over," Prandelli said.
"Perhaps we could have got back into the game at the start of the second half, we had two chances but of course once Thiago Motta went off injured, we didn't have anything left in the tank."
