Midfielder Milner netted City's fourth in Saturday's 4-2 win at Craven Cottage as the visitors responded from seeing their 2-0 lead evaporate before going up a gear to triumph and sit one point behind leaders Liverpool.
"When they got two back we really had to dig in," Milner told mcfc.co.uk.
"To come back again and show the character to kick on and get the two goals was pleasing.
"It's a good start to the festive period. A lot of games coming up, but if we can keep that desire and that will to win up, that will get you most of the way."
City were coasting at half-time courtesy of Yaya Toure's excellent free-kick and Vincent Kompany's goal, but Kieran Richardson pulled one back early in the second half before City captain Kompany spectacularly sliced into his own net.
Jesus Navas restored the visitors' advantage before his fellow substitute Milner converted a delightful cross from Alvaro Negredo to seal victory and kill off any Fulham hopes of a reply.
"He's got great ability," said Milner of Negredo.
"He doesn't really need to use his right foot, his left foot's that good. He can do anything with it.
"It was all made in the ball really. I just had to make sure I got a bit of contact on it.
"I was pleased to see it go in, it just gave us that cushion for the last few minutes."
It was City's third away win from nine games this season, a statistic which contrasts starkly with their 100 per cent home record from eight matches.
That perfect record will be tested on Thursday against Liverpool and the rampaging Luis Suarez.
City boss Manuel Pellegrini insisted the losses at Cardiff, Aston Villa, Chelsea and Sunderland were not relevant as his team had proved themselves on the road, including against European champions Bayern Munich.
He said: "We continue to ask why we don't play away like we do at home, but we've won three Champions League games away, two in the Capital One Cup and in our last three away Premier League matches we won two and have drawn one.
"We cannot continue talking about Cardiff and Aston Villa."
Fulham have lost nine of their last 10 games - the win over Aston Villa the anomaly - but boss Rene Meulensteen is optimistic a change in fortunes will soon come.
Meulensteen said: "It's really hard for them to take, to put so much effort in and so much positivity in the way we play.
"We never lost that spirit and I said, 'listen we're playing well enough, if we get one goal back and we get the crowd going, who knows what happens?'
"It's just a shame when it gets to 2-2 that we didn't just steady the ship a little bit. I would've been very, very happy if it had finished 2-2.
"We're all aware of what position we're in, but we also know that if we keep playing like this and if we keep producing this sort of energy we're eventually going to get the points we deserve.
"At the moment we're conceding far too easily and too many goals and we don't take our chances that we get.
"But these are things we can work on. But the core, the backbone of the performance is good."
In the absence of Dimitar Berbatov, who picked up a groin injury in training on Friday, Adel Taarabt led the line.
"He did exceptionally well," Meulensteen added.
"Adel is a guy that is full of creativity and energy going forwards. We used him where he's good."
Next Fulham travel to Norwich and Hull in matches which could see the momentum shift before the year's end.
"There are a lot of positives to take into the games against Norwich and Hull," Meulensteen said.