Voltar
The Bluebirds, who had won five National League games in a row, failed to break down City - two leagues below them in the English pyramid - and they will now head to Meadow Park on Tuesday night (October 20).
They will already know their potential first-round opponent with the draw taking place on Monday evening.
And reflecting on the goalless draw, Murray said: “It was a frustrating afternoon. But I still think we did enough to win it.
“I had a sly smile to myself because the atmosphere at this place has changed.
“You want to win every game, don’t you? But in football you can't win every game. We’ve been on a great run and it's another game unbeaten."
It is now a near 450-mile round trip added to the schedule ahead of hosting Forest Green Rovers on Saturday.
Murray added: “At the start of the season there was an anxiety about every mistake, every misplaced pass. There was a fear of losing and now there’s a demand to win.
“I love that because it’s a total shift in atmosphere. This club now demands to win football matches and they haven’t been able to say that for a very long time.
“We’ve come a long way and we look forward to Tuesday. It’s the FA Cup, enjoy the journey. This is what it’s all about."
Murray felt the result is a good learning curve for his players, who have been on a run of highs in recent weeks.
“It’s important we're real about where we are. Just because we’ve won a couple of games, it doesn’t give you the right to win every game.
“FA Cup’s always tough, especially when you play somebody from the lower leagues because they come with nothing to lose and that makes them dangerous.
“Credit to them, I thought they were very organised and came with a game plan. It was a really low block which we found hard to break down.
“We played against 11 men defending their goal and who were good on the break.
“It is what it is, you can’t win them all. If you don’t win, don’t lose. We’re into the hat on Monday and go to a replay Tuesday.”
The coach branded some of the team's decision making on the day as 'awful'.
“First half we have to convert one of those box entries. The amount of times the ball is in the box is crazy and we have to score one of them.
“It’s tough when you’re trying to break down a back six. It’s not that easy. You see that at every level of football.
“When you get those moments you have to punish them and we have those moments in the first half.
“I haven’t looked at any results. I’d imagine there were some surprises in the cup because there always is and we’re not one of them.”