I believe he wanted Perisic because he would have brought something different on the table. He's primarily a creative player, not a play-maker of any kind, but an option in the attacking half that will look to create for others more than himself. He's also a good crosser of the ball (with the left foot) and, in our case, good suggests that you can't allow him time and space to raise his head and aim. We don't have these qualities in our team. Both Rashford and Martial look more to create chances for themselves while Lukaku is at his best when he receives the ball at the end of moves and while facing the goal.
Most times (not always) Mourinho's attacking plan in the post-counter phase is based on overloading one side. He looks to open up spaces with off the ball movement and passes through a rhomboid shape that consists of the winger (who hugs the touchline), the #10, the more creative CM (in his 4231) and the forward (the FB has a more auxiliary role but can also contribute). The threat of a good cross draws opposition defenders and can potentially open up the channel between the FB and CB for our midfielder to run into. In our case, this player would have been Pogba. The threat from the wide areas would also make the CBs more alert of Lukaku's movement in the box.
Another strong aspect of Perisic's game is the diagonal off the ball movement towards the far post when the attacking play is happening on the other side of the pitch. This is a move that all our attacking options don't seem able to reproduce on a constant basis. In the end, Perisic isn't a world class player but he would have offered us three options that we currently can't create for ourselves: direct threat from out-wide, a good footballing brain among players who prefer to end moves rather than start them and the ability to stretch the opposition defense and open up spaces for others to attack. Just look at how we try to overload the left side in order to get one of Rash/Tony (mainly) in the half-space where they can cross it to Lukaku (again, mainly) at the far post. When we achieve this, it usually ends up with a goal (see our past few games, most of our not counter-attack goals come from that move). But because Lukaku can't contribute much in the link-up plays the positioning is very static (which makes it easier to defend against) and because we don't have a naturally left-footed player to cross the ball well, we have to work harder in order to get the reversed winger in a good position in the left half-space. Add to that the fact that most of our options are more attackers than creators and that our best creative players are poor in tight spaces and you'll see why it really becomes a struggle for us to string three passes together.