Mallinder’s men, shorn of a host of international stars, were 10-6 up at the break, but eventually succumbed, falling to a 29-20 defeat.
Saracens will now face Wasps in the semi-final at the Madejski Stadium on April 23.
But Mallinder, who saw Ken Pisi and Courtney Lawes score for his side, said: “It was a very good performance and I was proud of the players.
“We came here with an attitude that we were going to play, not be intimidated and for 60 minutes we did pretty well.
“Our defence was outstanding. We got some brilliant turnovers, helped by a very impressive back row. All three of those players put their hands up.
“In terms of attack, we played well. We looked to attack them, offload, not run into brick walls.
“I suppose we’ll look back at the try we didn’t get down the wing with Jamie Elliott.
“It’s disappointing to lose, but we’re proud of the performance.”
Saints were without Dylan Hartley, Kieran Brookes and Lee Dickson due to head injuries, while they lost George North to a swollen knee and Tom Wood to a shoulder problem in the build-up to the game.
And they were also struck by injury during the match as Ben Foden was forced off with a groin problem.
Nevertheless, Saints produced a fine performance for a long spell.
But Mallinder said: “I keep thinking back to 50, 60 minutes. We had a couple of lineouts in their half, seemed to get on the front foot and then couldn’t do anything with the ball.
“We got caught in a bit of a dogfight there and they’re very, very strong in that area of defence.
“Maybe if we’d had our international players we’d have been stronger in that final 15 minutes, but who knows.”