The weekend's result looks to have come as a relief, with Ian McParland and his players stating the importance of the victory. 
Notts' boss did not want to foresee whether this was going to be the end of the side's bad patch, saying: "I am delighted for the lads because we had a bad week with the three defeats and their heads got a little bit down.
"Time will tell if this is going to be the start of another unbeaten run.
"I thought the lads were professional about it. They treated them with a lot of respect and they stuck to their jobs.
"We had a lot of the ball and we passed it about well.
"I am delighted with a clean-sheet. We kept it tight at the back and I would have taken a 1-0 any day of the week before the game because it was a tricky tie.
"We were always going to be put under a bit of pressure because it was their big day, just like if we draw a Premiership or Championship club.
"It would be nice to get a good draw at home now to try to get in with the big boys in the third round."
Richard Butcher, who grabbed his sixth of the season to win the game for County was also reserved in his outlook for the next game.
He did, however, declare that the side must learn to shut teams out again and steal a few wins by the odd goal.
"It's easy to say we have won and that should kick-start us in the league now. But every game is different and we have got to go to Barnet and be on the top of our game," he said.
"If they beat us they go above us, and we don't want that to happen.
"Being able to grind out a 1-0 win is important for our league form because it was important not to give anyone any ammunition to have a pop at us."
On-loan defender, John Thompson also spoke of his delight at the clean sheet and praised the team's professional display.
He revealed: "They are such hard games to play in. I have been involved in quite a few over the years.
"We thought going into the game that our class would show eventually.
"But it doesn't matter who you are playing, they are always going to have spells when they are on top and they had theirs during the game.
"We could easily have come down here and been the upset of the round but I am just delighted by how professional the lads were."
Sutton United's manager, Paul Doswell was relatively impressed by his side's defensive display, ruing the one clear cut chance that he felt his side gave away.
He said: "The goal was the one piece of quality in the game. We knew Butcher makes those types of runs but we switched off and he scored a good goal.
"But our keeper did not have to make too many saves. It is a bizarre feeling to lose when I know my players gave it their all.
"Before the game we felt we were good enough to maybe get a replay and give it a good go at Meadow Lane.
"The biggest disappointment is that we didn't create enough clear-cut chances to score."
The Magpies next match is away at Barnet, where they will be looking to put a stop to their losing streak in the league.
*Quotes taken from the Nottingham Evening Post.