BBC Sport's Steve Cram on Britain's athletics prospects in 2012
It meant a relay double for the US following the women's 4x400m gold earlier on Saturday.
Briton Rooney, who ran an impressive leg in 43.80, said: "I came here for the medal but I'm gutted again. We just weren't good enough on the day."
It was the fastest showing for a US relay since a world-record effort of 2 min 54.29 sec at the 1993 World Championships in Stuttgart.
Wariner, who ran the anchor leg, said: "We all just gave it our all and ran an Olympic record.
"It was close to the world record, the fastest time since then. We have a lot more to come."
Video - Rooney 'gutted' to miss out on relay medal
The US men's team have won the event 16 times in 21 attempts, including 11 of the past 13.
Rooney, who did well to chase down Russia on his anchor run, added: "I knew I was capable of catching people, but when you're further down you have to go through more people.
"After yesterday I thought we could get silver, but to run 2.58 and not medal is so disappointing - it's a bad day.
"Hopefully there will be more competition for places next year, and with more people running 45s, we'll have a team running 2.56, 2.57."
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