United looked on track for a comfortable evening in Wales, as goals from Fernandes and Kobbie Mainoo put them in charge inside the opening 15 minutes, but League Two side Newport battled back and got themselves level shortly after the restart.
The FA Cup is United's last hope of winning silverware this season, with their Champions League and League Cup campaigns over, and the club sitting 16 points off the pace set by Liverpool at the top of the Premier League. They will travel to face either Bristol City or Nottingham Forest in the fifth round.
United reached the final of the competition last season, as Fernandes scored from the penalty spot, but it was not enough as rivals Manchester City secured a 2-1 win on their way to the Treble. The United captain hopes another deep FA Cup run can help salvage what has been a poor campaign to date.
"We have to understand that the FA Cup is our chance to win a trophy," Fernandes told BBC One.
"We have to give everything to get into the final step by step, game by game but we know that to make the season look not as bad as it has been. we have to try to win this trophy because it is important for us.
"We have been in the final last year. Unfortunately we did not get the trophy. We know how much the FA Cup means for our fans, our club, for the country so we know how important it is and it's important for us too. We want to get into the final and win."