But substitute Chris Burke pulled a goal back for the visitors and defender Gabor Gyepes rammed home the equaliser a minute from time to leave them needing a solitary point to secure their place in the play-offs.
"Saturday was a freak result. At this stage of the season you will get them," said Jones.
"It was one of those days where you think nothing is going to go for you - and it was the same tonight for an hour.
"It was a sombre place and we had to rise above that and after an hour we did.
"If we didn't show grit and determination on Saturday then it came flooding back tonight and we deserved to come back into it."
Teenage star Jonjo Shelvey put Charlton ahead before the interval, toe-poking in Lloyd Sam's cross.
Joe Ledley saw a 35-yard volley pushed onto the crossbar by Rob Elliot and Jay Bothroyd had a goal disallowed for a push, and Cardiff looked beaten when Nicky Bailey rifled in the second in the 80th minute.
But Charlton, who blew a two-goal lead against Blackpool on Saturday - the day they were consigned to the drop, allowed Burke to burst through and pull one back.
And the almost inevitable equaliser came when Burke's corner was flicked on by Roger Johnson and Gyepes swept the ball home.
"It would have been hard to come away with nothing today because it would have been tough to pick them up and we've got a hard game on Saturday against Ipswich," added Jones.
"If we had gone into that on the back of two defeats it would have been a nervous occasion.
"But if we've got to limp over the line then we will. We've got to get another point."
Charlton did stretch their belated unbeaten run to six matches, but there were still a few calls for manager Phil Parkinson to go once the equaliser flew in.
"I had an experienced team out there and yet we still looked naive," admitted Parkinson.
"We're a team scarred from the season, when it's happened before, and tonight we went into panic mode on and off the ball.
"Cardiff are a good side and I expected a reaction from the weekend and we got that.
"It was a tight game, we got the second goal and that should have been enough. The reaction from the supporters is understandable, I'd be feeling the same if I was sat there."