Kagawa struck just before the break at Old Trafford then added two more in the second half to inspire the win before Wayne Rooney added a long-range strike in the final minute.
The victory sees United stretch their lead at the top of the Premier League to 15 points and Ferguson was full of praise for the Japan international, who arrived at the club from Borussia Dortmund last summer.
He told Sky Sports of the forward, who was out with injury earlier in the season: "He's a good finisher, the lad. His second and third goals were terrific and he showed great intelligence for the first one and composure.
"He's gradually getting his form back because he missed that period of football in October and November which set him back a little bit.
"He's going to be a good player. Next year he'll be far, far better too."
Ferguson was also pleased with Rooney, who was making his first start following a sinus problem after appearing as a substitute in the win over QPR last week.
The boss added: "He needed a full game, he came on a sub last week. Scoring a goal is always important for strikers and it'll help his confidence."
Ferguson was relieved his players all appeared to come through the encounter unscathed, with the second leg of their UEFA Champions League tie against Real Madrid looming in midweek.
There were some close calls when Robin van Persie appeared to hurt himself stretching to set up the opening goal, while Patrice Evra and Danny Welbeck were victims of physical challenges from the visitors.
"There was a few hefty tackles out there today," Ferguson added. "It was surprising; normally the pitch is too big for that kind of football. Everyone is ok I think."
After seeing United stretch their lead to 15 points, Ferguson says there is no need for his side to be looking over their shoulders for nearest rivals Manchester City.
"I think the best way for us to handle it is to win our games," he added. "Win our next game and then our next game - that's the way to do it.
"We don't need to look back. Look at our team at the moment, they're playing with a great spirit and there's a great atmosphere in the dressing room that's helping us.
"No matter which games are coming up, we're relishing it."