A search for heavy pseudoscalar (A) and scalar (H) Higgs bosons decaying into a top quark pair (t¯t) has been performed with 20.3 fb−1 of proton-proton collision data collected by the ATLAS experiment at the Large Hadron Collider at a center-of-mass energy √s=8 TeV. Interference effects between the signal process and standard model t¯t production, which are expected to distort the signal shape from a single peak to a peak-dip structure, are taken into account. No significant deviation from the standard model prediction is observed in the t¯t invariant mass spectrum in final states with an electron or muon, large missing transverse momentum, and at least four jets. The results are interpreted within the context of a type-II two-Higgs-doublet model. Exclusion limits on the signal strength are derived as a function of the mass mA/H and the ratio of the vacuum expectation values of the two Higgs fields, tan β, for mA/H >500 GeV.