I would call in to question the origin of this phrase. At first glance it seems highly romanticized - something that has been attributed to Attila (perhaps centuries) after his death by judicious use of poetic license.
One of the main primary sources for Attila is Priscus - who seems to actually have spent a great deal of time with Attila and is regarded as a rather reliable source. His most famous work - The History of Byzantium - has only survived in parts. This translation from Fragmenta Historicorum Graecorum deals with part of his time spent with Attila, but there is no mention of these words in the text that I can find.
Other sources, such as Jordanes, who wrote Getica, also makes no mention of this quote.
A quick Google search hasn't turned up any answers as to who first attributed to Attila, but it doesn't appear to be coined by any of his contemporaries, or near contemporaries.
It certainly sounds like something a civilized barbarian and the Scourge of God would say, but it's something I highly doubt he actually said. Makes a great story though.