The visitors had no answers to a fierce first-half onslaught from the Saints which saw them build a 27-3 half-time lead and snap a two-game losing streak.
"After last week's defeat we got a good reaction, the first half in particular," Mallinder said.
"We had a good set-piece, took our opportunities and our defence was excellent.
"I told them in the week, 'Let's not panic, we are on a good run in the league and although we gifted the Scarlets four tries last week we are not a million miles off'.
"Saracens was a good game to play today as they have a fantastic away record and it was just what we needed."
The only disappointment for Saints was their failure to secure a bonus point for a fourth try, but Mallinder added: "You've just got to ensure that you win the game.
"Sale lost last night from being well ahead."
Saracens coach Mark McCall felt it was a game of two halves from his side.
"I'm very disappointed," McCall said. "Everything that could go wrong in the first half went wrong.
"For the first try we missed three or four tackles on Ben Foden and they went away and scored.
"We did not react to that setback and you can't do that against a side as good as Northampton."
Saracens edged the second half 5-3 and McCall added: "The game was done and dusted by half-time but we regrouped well and did well to deprive them of a bonus point.
"We could have easily folded."
Mallinder has been linked with the vacant England post since Martin Johnson stepped down, but he added: "I love it here, it's a fantastic team and getting better.
"It would have to be a big offer to get me away from here. I'm 45 but at some stage in my career I would love to coach England, but I have heard nothing yet."
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