It looked as if the Robins were on their way to a vital win thanks to Sam Baldock's penalty, but it is they who stay at the bottom.
City took control in the latter stages of the first half with Notts County goalkeeper Bartosz Bialkowski making a good block to deny Baldock, who was through one-on-one.
Bialkowski was then under bombardment for the next five minutes as he first denied Jay Emmanuel-Thomas before instinctively keeping out Baldock's close-range effort.
The Robins struck while on top through a penalty from Baldock, although the decision to penalise Dean Leacock for pushing Aden Flint did look harsh.
County pressed in the second half and they got out of jail in the 89th minute when Marvin Elliott was judged to have held Leacock, with Sheehan making no mistake from the spot.