The 47-year-old, who left his post as Wales head coach to take over at the Stadium of Light this week, could not prevent a 2-1 defeat at Villa Park that leaves Sunderland deep in the relegation mire.
Albert Adomah's third goal in two games and a deflected strike from Josh Onomah were enough for the home side, which moved into fourth in the table.
Lewis Grabban gave Sunderland a lifeline in the second half but it could not muster the equaliser that would have taken it to within three points of safety.
It could have been worse for Coleman and the Black Cats had relegation rival Bolton not surrendered a two-goal lead against Reading, with Liam Moore and Leandro Bacuna scoring in the final 14 minutes at the Macron Stadium to keep the host in the bottom three.
Meanwhile, Coleman's old club Fulham denied Sheffield United the chance to go top of the table as they won a nine-goal thriller at Bramall Lane.
Leon Clarke put the host ahead before goals from Sheyi Ojo and Ryan Sessegnon made it 2-1 to the visitor, with the 17-year-old scoring again before half-time to keep his side in front after Clarke had snatched a quick equaliser.
Ojo got his second after 69 minutes and the highly rated Sessegnon clinched his hat-trick to make it 5-2, but Samir Carruthers struck in the 86th minute and Clarke completed his own treble in stoppage time to set up a nervy finish.
Fulham held on for a win that takes it above Norwich into 14th place, though, and United's spirits was further dampened with the news that Cardiff had leapfrogged it to go second thanks to Callum Paterson's solitary goal away to Barnsley.
Burton moved a point nearer to 21st-placed Birmingham City with a 1-1 draw at Brentford, although Ben Turner's equaliser was not enough to lift them out of the relegation zone.
Norwich City and Bristol City had disappointing results, Reading snatched a draw at Bolton Wanderers and there were stalemates between Millwall and Hull City, and Brentford and Burton Albion.