In what was his first league game in charge since taking over from Kevin Nolan last week, Kewell saw red for arguing with officials following Exeter's fourth goal midway through the second half.
After Pierce Sweeney and Jayden Stockley helped Exeter to an early 2-0 lead, Enzio Boldewijn gave Notts hope heading into half-time, before Sweeney, Stockley and Aaron Martin put the result beyond doubt.
The defeat is Kewell's second as Notts manager, after being knocked out of the Football League Trophy with a 2-1 midweek defeat to Grimsby Town, and the Socceroos legend was far from pleased.
"We went in at 2-1 and it was game on," Kewell said after the game.
"I was confident we were going to get something out of the game. But another set-piece and a mistake and we are 3-1 down. That is when the anger kicked in.
"The eagle-eyed referee sees another handball, gives it to them and they miss it so we are still in it. Then there was a cross in the box and it was one of those 'does it hit his hand, or does it not?'. The referee says no, we are complaining, they go up the other end and score a goal.
"That was disappointing and that is when I get my marching orders. I said 'well done' to the referee; I said you can see one in the far corner but not one straight in front of you.
"I'm a winner, we are going to have to try things, and to be vulnerable at the back to get extra men in the box.
"I'm giving players a crash course in playing in certain positions - but we have to deal with what we are dealt with, we have a lot of players playing in places they aren't used to."
Kewell's Notts, who remain winless after seven games as a result, are next in action against Stevenage on Sunday September 16.
