It was not a convincing performance from the Saints as they let a 12-0 lead slip away to trail 13-12 at the interval, but second-half tries from Luther Burrell and Dylan Hartley eventually saw them home.
"Our performance was a mixed bag," Mallinder said.
"We were good in the first 20 minutes scoring two good tries but then we relaxed, kicked loosely and going down to 14 men put us under some considerable pressure.
"However we kept our cool in the first 10 minutes of the second half and then our forwards went on to dominate."
Northampton would have won more comfortably had Ryan Lamb not been off form with his goal kicking, and the outside half was substituted for Stephen Myler early in the second half.
Mallinder said: "We have two good number 10s, Lamb missed a couple of kicks as their kicker did.
"Stephen is a steady head and controlled the game when he came on and had a big hand in our crucial try."
The Saints coach also paid tribute to skipper Hartley, who was man of the match after picking up his second try in as many fixtures.
"Dylan stands out with his attitude, he doesn't have a sloppy session he is always the first there and the hardest there," he said.
Hartley himself was happy to get past a stubborn Exeter side.
"We knew Exeter are a good team and that they play for the full 80 minutes," said the England international.
"Last week against Gloucester we got a bit loose and were lucky to come away with a win. Today when it got tough we returned to the driving maul and hammered home our advantage."
Exeter coach Rob Baxter was able to take many positives from the defeat, with Phil Dollman and Matt Jess both dotting down to run their hosts close.
"I am pretty pleased," he said. "On the two previous occasions here we have been comfortably defeated.
"Last season we lost 33-3 but today we were in the lead at half-time and were competitive to the end.
"It was by far our best performance here and we made it very edgy for Northampton right up until the end.
"However, we kicked away too much possession in the first quarter but after that we looked a good side and kept playing with tempo."
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