The Red Devils appeared to be slipping out of contention at home and abroad under the guidance of Jose Mourinho.
The Portuguese has, however, been relieved of his duties and replaced by Ole Gunnar Solskjaer on an initial interim deal through to the end of the season.
He opened his reign with a 5-1 victory over Cardiff, helping to return a sense of optimism at Old Trafford for those on and off the field.
Quizzed on whether an eight-point gap to the Premier League’s top four can be bridged with a feel-good factor flooding back, Valencia told MUTV: “Absolutely.
“Nobody is giving up at all. You know there is half a season left to play so it’s all about working hard, battling and playing well.
”We know we have got the quality within the squad to be able to do that. It is all about being focused and the aim is still to get into those top four places.
“We also want to go as far as we can in the Champions League – why not get to the final? Why not try to win the two cup competitions we are still involved in?”
That may sound slightly ambitious for a side that stumbled out of the blocks in 2018-19, but United are expected to challenge for major honours across any given campaign.
Momentum will need to be built if they are to compete for silverware this term, but they have another very winnable game approaching on Boxing Day against struggling Huddersfield.
Valencia added on a contest which will see the Red Devils take to home soil for the first time under Solskjaer: “I think it is good.
“The main thing is to get everyone together at Old Trafford after Christmas and it is a great fact we don’t have to travel as it’s on our doorstep. Playing in front of our fans is always a special occasion.
”We are getting the chance to make them happy and hopefully put any recent bad results behind us to get into good form again.
“We need to start putting a string of wins together and putting in a good performance to make the fans happy.”