A search for Higgs boson production in association with a pair of top quarks ($t\bar{t}H$) is performed, where the Higgs boson decays to $b\bar{b}$, and both top quarks decay hadronically. The data used correspond to an integrated luminosity of 20.3 fb$^{-1}$ of $pp$ collisions at $\sqrt{s}=8$ TeV collected with the ATLAS detector at the Large Hadron Collider. The search selects events with at least six energetic jets and uses a boosted decision tree algorithm to discriminate between signal and Standard Model background. The dominant multijet background is estimated using a dedicated data-driven technique. For a Higgs boson mass of 125 GeV, an upper limit of 6.4 (5.4) times the Standard Model cross section is observed (expected) at 95% confidence level. The best-fit value for the signal strength is $\mu = 1.6 \pm 2.6$ times the Standard Model expectation for $m_{H} = 125$ GeV. Combining all $t\bar{t}H$ searches carried out by ATLAS at $\sqrt{s}=8$ and 7 TeV, an observed (expected) upper limit of 3.1 (1.4) times the Standard Model expectation is obtained at 95% confidence level, with a signal strength $\mu = 1.7 \pm 0.8$.