City were hoping to mark their new era with a win, but in the end could well have lost.
Dowie was able to field the line-up which had won so impressively at West Bromwich Albion. Michael Mifsud had missed the game at Hillsborough which was abandoned because of a waterlogged pitch, but he had recovered from his hamstring injury in time to start.
The returning Stern John thought his afternoon had got off to a perfect start when he netted after just five minutes but he had been stranding in an offside position when the ball came to him.
The Trinidad and Tobago international then curled a shot well wide when he should have done better.
Coventry were beginning to get joy down the left flank where Leon McKenzie was looking very sharp.
The former Norwich man forced Kelvin Davis into a save with a header from a Michael Doyle cross in the 15th minute.
The home side's increasing share of the play bore fruit in the 19th minute when Jay Tabb nodded them into the lead.
Again it was McKenzie who was the driving force. He was the first to react when the ball hit Jason Euell and, when his effort was kept out by Davis, Tabb was there to convert.
Both sides had other chances in the half but Coventry went in to the break with a deserved lead.
Southampton needed to show more and they did step up the pace after the break. They started to push Coventry back and spread the ball wide. A goal began to look likely and it came just before the hour mark.
Euell was fed by Youssef Safri and delivered an excellent cross which Bradley Wright-Phillips headed neatly home.
Suddenly it was the visitors that were forcing the pace and Wright-Phillips should have won the game in the 77th minute when Andrew Surman sent him clear with an excellent pass. But he seemed to hurry his shot and it rolled just wide of the target.
Coventry reshuffled their attack and, although it did work to an extent, they never looked likely to record a win.