Clearly, ATF didn't develop the practice of gun walking under the current administration. But Obama specifically referred to "the Fast and Furious program," which unquestionably started during his term as president. That operation was not "begun under the previous administration."
Perhaps the president made a mistake, and he really meant to talk about gun-walking in general instead of a particular gun-walking operation. But he could also be trying to wash his hands of any accountability for a program that launched on his watch and allowed 2,000 powerful firearms to end up on U.S. and Mexican streets.