In this paper we report a measurement of the tt̅ production cross section in pp̅ collisions at √s=1.96  TeV using data corresponding to an integrated luminosity of 2.2  fb-1 collected with the CDF II detector at the Tevatron accelerator. We select events with significant missing transverse energy and high jet multiplicity. This measurement vetoes the presence of explicitly identified electrons and muons, thus enhancing the tau contribution of tt̅ decays. Signal events are discriminated from the background using a neural network, and heavy flavor jets are identified by a secondary-vertex tagging algorithm. We measure a tt̅ production cross section of 7.99±0.55(stat)±0.76(syst)±0.46(lumi) pb, assuming a top mass mtop=172.5  GeV/c2, in agreement with previous measurements and standard model predictions.