Tony Pulis' side are on an unbeaten run of 10 Premier League games and have not lost at the Britannia Stadium in the league since February 4.
Both those records looked set to come to an end when they trailed Southampton 3-1 at half-time on Saturday and were still a goal behind, and down to 10 men, heading into the 90th minute.
But substitute Cameron Jerome proved to be the hero with a stunning 30-yard volley that earned Stoke a point and kept them in eighth.
They make the short journey up the M6 to the Etihad Stadium on Tuesday to take on the reigning champions, who will hope to close the seven-point gap to leaders Manchester United.
Jones said: "We are doing well. We had a few slip-ups but credit to the team, the manager and the fans for the run we have been on.
"The next game is the most important game for us because we're going to the home of the champions.
"Here at Stoke City we play for 90 minutes. If we get beat, we get beat, but we'll never give up. That comes from pride.
"This is our job. No-one wants to lose so you're not just going to stand there and accept defeat."
History is not on Stoke's side, with the Potters having failed even to score a goal at the Etihad Stadium in the league since promotion to the top flight in 2008, suffering four defeats and conceding 11 goals.
Jerome admits they let their standards slip against Southampton on the back of a great performance against Liverpool on Boxing Day, which earned them a 3-1 win.
The striker said: "We set our benchmark high against Liverpool on Wednesday. That was a tremendous performance but this was a little bit sloppy. The games come thick and fast over the Christmas period and we have to be a little bit sharper.
"We probably didn't show Southampton as much respect as we should have. This is the Premier League and there are some really good teams in it."
Jerome rated the goal as the best he had ever scored as he lashed the ball in off the underside of the bar with a ferocious strike.
He said: "There was one that Pete (Crouch) could have laid off to me before. I was kind of angry with him and that's why I smashed it so hard.
"I knew it had a chance. I thought it was going to go straight in without the bar, but when it hit the bar I thought it was going to come out. Luckily the spin took it back in.
"But the most important thing is the point. It keeps the unbeaten run going and keeps the momentum in the camp as well."
The goal is unlikely to be enough to earn Jerome a spot in the starting line-up, though, with Jonathan Walters and Jones currently Pulis' preferred strike pairing.
Jerome has made only seven starts for the Potters in the Premier League since joining the club from Birmingham last summer, but he said: "I'll always keep working hard.
"If an opportunity comes I'll stick it away if I can. But we have a good squad at the minute. The manager chooses his team and you just have to accept that. You just have to go out and play your best for the team when you come on."
Stoke were unusually vulnerable defensively on Saturday but they have captain Ryan Shawcross and full-back Geoff Cameron available again after serving one-match suspensions.
Midfielder Steven Nzonzi is also free to play after Stoke appealed the red card he was shown in the second half, with a decision on whether he will have to serve a three-match ban likely to come on Wednesday.