Jones was then scythed down in the 43rd minute by Lee Hills, who was duly sent off, and Deeney added a third for Walsall with 10 minutes remaining.
Penney, whose team had won on their last four visits to Walsall, said: "We were just not ruthless enough in both boxes.
"We were second best so we need to get it right for Leeds who we play next Tuesday.
"We had players out injured and two with flu symptoms, but we were poor. We needed to stand up and be counted but not enough did."