Los Che looked set for a lifeline in pursuit of the last-16 with United heading for a draw heading into the closing stages against the Swiss minnows.
But Fellaini struck late on to confirm United's progression to the knockout stages at the expense of Valencia, the goal being allowed to stand despite the Belgian appearing to handle the ball.
United head to Valencia on Wednesday with no pressure having already made sure of qualification, and though the hosts will be eager for some form of retribution, Soler is not shying away from the fact he and his team-mates were extremely irritated by Fellaini's goal.
"I don't think it [the Fellaini goal] alone was what deprived us of having a chance [of progression], but the hand is there," Soler told reporters. "They are things that do not depend on us.
"Obviously we are a bit p****d off with the situation, but we cannot change it so we will have to look forward."
2 years ago, a year old @Carlos10Soler debuted with Valencia CF in official competition. 2 years later he's become one of the pillars of our team. The truth is that the best for him is yet to come pic.twitter.com/nOBLOioc6Y— Valencia CF English (@valenciacf_en) December 10, 2018
Wednesday's game will see Juan Mata return to Mestalla and Soler – who looked up to the United player during his time at the Spanish club – is excited about playing against him in Valencia's famous stadium.
"When I played in the academy as a kid, Juan was here and played in the same position, so I looked up to him a lot," he said.
"In the first leg, I swapped shirts with him and it will always be a memory. I've seen him a lot in Mestalla and facing him there will be nice."
Valencia coach Marcelino Garcia Toral will also be going up against a familiar face in Eric Bailly, the pair having worked at Villarreal.
Despite having spells of inconsistency and bad injuries, Marcelino is convinced the defender will be a success at Old Trafford in the long run.
"I was lucky to have him as a footballer," Marcelino said of Bailly. "He is a great player and an extraordinary person.
"I sympathise with the injuries he is going through because it is difficult to increase performance, but I wish him well and for him to find a great condition.
"With his professionalism, his way of being and his youth, he will surely succeed in Manchester. He has played great games, but because of the injuries he is not having the necessary continuity."