SR71 didn't. It was refuelled. It was a rather crude aeroplane, though it has to be realised that Kelly Johnson had to throw something together quickly for the US spy plane program so not really comparable to the long development programme Concorde got. Many SR71s were lost, all through technical problems. Did you know it even had to dive to go supersonic? It couldn't overcome transonic drag in level flight! Concorde climbed through that phase of flight!
The US really should have used some Concordes to do the job the SR71 did. Sure, it was a Mach 2 aeroplane rather than Mach 3, but Mach 2 was fast enough not to get shot down (ask any Lighning pilot who tried to get a bead on it!). And it didn't need special fuels or have a leaky titanium airframe with unstart-prone engines (which caused mny of the SR71's losses).