United were held to a 0-0 draw at Old Trafford by a well-drilled Albion side who sat deep virtually throughout the contest.
It was the eighth time in the Premier League this season the Red Devils have had to settle for a point from a home game, which has included other 0-0 stalemates against Hull and Burnley and 1-1 draws with Bournemouth and Stoke.
And, regarding the Baggies match, United midfielder Fellaini told MUTV: "It's disappointing, everyone is disappointed. We've lost a lot of points like that, but that's football and we have to keep fighting. We have to improve on that."
He added: "When you play away, the other team tries to attack.
"It's not easy to play at Old Trafford, they came to take a point or win with a counter-attack.
"But we have to find a solution to win the game."
The result, while extending their unbeaten run in the league to 19 games, struck a blow to fifth-placed United's bid to secure a top-four finish this term, a battle that will resume on Tuesday when they play at home once again, hosting Fellaini's former club Everton.
They then go up against their old manager David Moyes when they face rock-bottom Sunderland away on Sunday as their schedule of nine matches in April in all competitions continues.
Fellaini said: "There are 10 games (left in the league for United), 30 points so we have to keep going.
"There are a lot of big games coming and we have to be ready. There are six points available next week and I hope we can take them.
"It (the match against Everton) will be a tough game. They're a tough team but every game will be difficult and we have to fight to the end."