And there was also disappointment for Ward, beaten 6-4, 6-3, 6-4 by Andreas Seppi, a player ranked 127 places above him.
It means Italy will now face Switzerland or Kazakhstan in the final four while Great Britain return to World Group round one in 2015.
"He played some great tennis at important periods in the match and that was the main difference in the end," said Murray, who won his last match against Fognini, on clay, five years ago.
"When I had my opportunities I was a little bit disappointed in myself that I couldn't take them. When he had his, he was exceptional, so all credit to him.
"We don't get that atmosphere on a day-to-day basis on the ATP Tour but when you play away from home you get that."
Murray did express frustration that Italian team captain Corrado Barazzutti was speaking while he was serving but refused to blame defeat on the partisan home crowd, preferring to highlight how this had been Britain's best Davis Cup campaign in 28 years.
- Sports & Recreation
- Fabio Fognini
- Andreas Seppi