The 19-year-old Stokes struck in the third minute of injury time to end his side's eight-game wait for a Barclays Premier League victory and dash new Rams manager Paul Jewell's hopes of a positive start to his reign.
Keane admitted he barely left his home after last Saturday's 7-1 horror show at Everton, but he forecast a brighter Sunday for his family this time.
Keane said: "I said last week, when you lose, everyone reacts in different ways.
"There's a good chance I will leave my house tomorrow. Everyone reacts in different ways.
"It does not mean I will be skipping around the place, but at least I can leave the house, which will be a relief for my family, no doubt."
The game looked destined for stalemate until Derby goalkeeper Stephen Bywater parried Kenwyne Jones' late header and blocked Stokes' follow-up before the young striker hooked the ball into the net.
Jones had hit the post from just two yards out in stoppage time at the end of the first half, but Ward had earlier tipped a Kenny Miller shot on to the woodwork at the other end and seen Dean Whitehead clear Steve Howard's effort off the line.
Asked if relief was his overriding emotion, Keane said: "Relief? I can't find the word. Delighted? Happy? No, I am not relieved, but happy.
"It don't think it was ever going to be a classic. You probably think it has got a 0-0 draw written all over it and I suppose we would have had to accept that with two minutes to go.
"Maybe we had a little bit of luck today, but I don't think we have had too much this season, so we have to take it when it comes.
"I am happy for everyone at the club because it has been a long week for everyone, there's no getting away from that."
Derby boss Jewell was devastated to see a point slip away at the death just when he thought it was in the bag.
He said: "It's a real kick in the teeth when it happens like that. You are disappointed when it looks like you are earning a draw.
"There was not a lot of quality in the game, although we showed some decent stuff.
"We were disappointed to lose, but the players gave me everything and I cannot be critical of them as far as effort is concerned."