He called Coutinho's contributions "the most important thing right now" and said it is "not fair" to ask him questions about his future, reiterating: "He gives us his all every game and that's all we can ask him".
United spurned opportunities to kill the game off when Rashford slashed a right-footed shot wide in the 57th minute and Lingard fired straight at West Brom goalkeeper Ben Foster.
"We scored a fantastic first goal... we could have scored more".
"We had a few chances to kill the game but I knew they would react", Mourinho added.
Liverpool are on 31 points, sandwiched between fourth-placed Tottenham Hotspur and sixth-placed Burnley with all three teams 18 points behind leaders City after 17 league games.
With memories still raw about squandering a 3-1 lead to lose 4-3 in this fixture a year ago, Liverpool didn't let up and Roberto Firmino completed the rout with a diving header off Coutinho's cross in the 66th minute.
It is advice the Liverpool manager is delighted to have listened to with Salah having already scored 19 goals this season.
Coutinho's goal was the highlight.
Firmino nearly doubled that lead with an effort which deflected wide after excellent work by the ever-dangerous Salah. Things could have been different, however, had Jermain Defoe found the net in the 39th - when the score was 2-0 - rather than strike the base of the post.