The Belgium international, who has failed to cement a regular spot in the United team following his £27m arrival from Everton last summer, was the subject of a tweet from the Baggies' official page while warming up at The Hawthorns.
Just before Fellaini came off the bench in the second half, with West Brom leading 1-0, Albion's Twitter account wrote: "Fellaini has now taken his tracksuit off, fortunately he has a Man Utd strip on underneath."
However, the joke backfired when Fellaini scored an equaliser just three minutes after entering the field.
In response to the tweet, Lindegaard wrote: "Complete lack of knowledge, class and respect on Twitter from WBAFCofficial on Fellaini!! #united #karma #keepbelieving."
West Brom later apologised by saying: "Sorry if a joke about a footballer not having a shirt on under his tracksuit top has caused such outrage. It was not intended as a slur."