Allardyce was appointed as Sunderland boss last week, taking over from Dick Advocaat, as the Black Cats look to get out of the drop-zone.
The Wearsiders have picked up just three points all season, and they are still winless, with Dowie bemoaning the state of their defence.
He said: "They've got some good players there. For me, defensively is the big issue. Can they keep clean-sheets? Sam is very, very good, like Tony Pulis, at finding a way of doing that. I think it's the perfect fit. Yes, it's a big challenge, but it's not insurmountable, by any stretch."
Sunderland have conceded more goals than any other team in the Premier League to date, with their defensive issues continuously costing them points.
In their most recent fixture, the Black Cats were 2-0 up against West Ham United, but they let their lead slip and ended up only being able to claim a point from the match.
That rather summed up their season so far, where Sunderland have had a tendency to give away cheap goals to opposition sides.
It leaves Allardyce with a big job to do, but the 60-year-old is famed for his ability to get teams organised and he will need to ensure that he finds a way of tightening up Sunderland's leaky defence quickly.