Mark Jones' side beat Bognor Regis Town 1-0 to earn a place in the FA Cup first round, just a week after dropping to 20th place in the National League South.
City's Matt Paterson scored the only goal of the game before he missed a penalty in the last action of the first-half.
Bognor finished the match with ten men after Calvin Davies was sent off with less than 15 minutes remaining.
There was a sense of relief afterwards from Jones, who said: "I think we deserved it. There was a bit of pressure on us going into today, things haven't been great for us in the league - we dropped into the bottom three last week. We had to produce.
"I questioned one or two of the lads in the week. What we've been producing hasn't come up with the right results. You could argue that it's been a little bit unjustly. I think they proved today that their attitude is good.
"I'm absolutely over the moon for us to be in the first round. It could be an important thing for the club, we're hoping for a good draw.
"We made some changes and went for a more basic shape. Off the ball has let us down this season, on it we've been great and scored plenty of goals.
"We got the clean sheet but we could have made it more comfortable for ourselves."