"A bit of 'backs to the wall' stuff, but you're proud of it because it was good vibes before the game.
"Guys had talked about having a good feeling. We had trained really well on Thursday.
"It was just like watching a different sort of team, I can't get over how fantastic the communication was."
Anthony Bell scored the opening goal in the first few minutes, and while Massey did not find the road as easy going they still scored twice to take a 2-1 lead into the break.
At halftime, City broke it down that they needed to move off the ball more, and if they were going to do so, it had to be set up properly.
It worked as Max Davidson grabbed the equaliser five minutes after the resumption, and then Dan Aplin put City ahead with 21 long minutes to go.
"They came at us at the end of the game, we scrambled really well," said Francis.
Keeper Glenn Graham scrambled desperately in goal, while Jack Jonas made a couple of telling tackles in the box, and then Eli Fleming produced an excellent turnover with time almost up.
Francis estimated his team could not have withstood the students scoring an equaliser and sending the match into extra time, as City were out on their feet.
They had a lot of heroes – Latham Berry was sick before the match but played the full game with four regulars already injured, while Ben Hussey, who along with Tom Dixon was drafted in to play at the higher level, had only promised Francis a strong 45 minutes but still gave him 90.
"After the last few weeks, I asked for a response, and I got the response we were looking for," said the coach.
"It'd be nice to go on a Cup run."
City stay alive in the elimination competition of which they were the inaugural winners in 2009.
Since then, their best effort has been to reach the quarterfinals, with first round exits being most common in recent seasons.
City will return to Federation League action this weekend when they host PN Marist at Wembley Park.