Measurements of dijet $pT$ correlations in Pb+Pb and $pp$ collisions at a nucleon-nucleon centre-of-mass energy of $s\mathrm{NN}=2.76 TeV$ are presented. The measurements are performed with the ATLAS detector at the Large Hadron Collider using Pb+Pb and $pp$ data samples corresponding to integrated luminosities of 0.14 nb$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ and 4.0 pb$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$, respectively. Jets are reconstructed using the anti-$kt$ algorithm with radius parameter values $R=0.3$ and $R=0.4$. A background subtraction procedure is applied to correct the jets for the large underlying event present in Pb+Pb collisions. The leading and sub-leading jet transverse momenta are denoted $pT1$ and $pT2$. An unfolding procedure is applied to the two-dimensional ($pT1$, $pT2$) distributions to account for experimental effects in the measurement of both jets. Distributions of $(1/N)\backslash mbox\{$\mathrm{d}$\}\; N/\backslash mbox\{$\mathrm{d}$\}\; x\_\{\backslash mathrm\{J\}\}$, where $xJ=pT2/pT1$, are presented as a function of $pT1$ and collision centrality. The distributions are found to be similar in peripheral Pb+Pb collisions and $pp$ collisions, but highly modified in central Pb+Pb collisions. Similar features are present in both the $R=0.3$ and $R=0.4$ results, indicating that the effects of the underlying event are properly accounted for in the measurement. The results are qualitatively consistent with expectations from partonic energy loss models.