United fell 11 points behind leaders Manchester City after losing the Manchester derby on Sunday (10 December), as Pep Guardiola's men brought their neighbours' 40-game unbeaten run at Old Trafford to an end.
City have won 15 of their last 16 league games so far, the best record at this stage of the season since the competition's inception in 1992, and they look head and shoulders above everyone else in the division.
However, despite their bitter rivals' sparkling form, United captain Valencia dismissed any suggestions the title race was already done and dusted.
"We are Manchester United and it's our duty to keep going to represent the club and keep looking forward and try to close that gap as best we can," he told Sky Sports.
"While ever there's a chance mathematically, we just keep fighting."
United know all too well what it feels like to squander a seemingly unavailable lead; they were pipped to the title on goal difference by City in 2012, having held an eight-point lead with six games left.
And Valencia believes United can draw on that experience to take the fight to their local rivals and ensure the title race goes down to the wire.
"We know that 11 points is a big gap but I can think back to when Sir Alex Ferguson was manager and the gap was something like nine [eight] points and we ended up losing the title," the Ecuadorian added.
"So we know that it's the Premier League, we know that everyone's capable of beating everyone else and it's just a case of keep fighting."
United will look to bounce back immediately from their derby defeat when they host Bournemouth at home on Wednesday night (13 December), with back-to-back trips to West Bromwich Albion and Leicester City either side of a visit to Bristol City in the Carabao Cup still to come before Christmas.
Following their trip to the King Power Stadium, the 20-time champions of England then face a further two games before the end of the year and December's frantic fixture schedule will likely see Jose Mourinho rotate his squad in the coming weeks.
The Portuguese has already hinted that promising young duo Scott McTominay and Axel Tuanzebe could soon be handed their league debuts.
"I have faith in them," he told MUTV. "Honestly, sometimes, I don't play them more because I have respect for some of the older players that are great professionals and are always ready for the team.
"But, in terms of their qualities, McTominay and Tuanzebe are ready, they are ready to play so I played them with 25, 30 minutes to go against CSKA [Moscow]. I played Scott against Benfica when we had not even yet qualified. I have lots of faith in both of them."