Thanks to a star performance from George Pisi, the Saints were in complete control at Franklin's Gardens as they opened up a 22-3 lead at the interval.
They carelessly lost control and received two needless yellow cards from referee David Rose, allowing the visitors back into the match, but held on for a 22-13 victory.
"I'm pleased with the win but frustrated not to pick up a bonus point," Mallinder said.
"We were very good in the first half - scoring three tries - and at half-time I told them to do exactly the same, but in the second half we forced it too much.
"We need to improve in closing out games and need to be more clinical in taking our opportunities."
Bath must have feared another heavy defeat at the interval but, aided by Northampton losing two players to the sin-bin, they gave a tenacious second-half performance which saw them keep the Saints scoreless.
Nevertheless, Bath could not avoid slipping to a fourth consecutive league defeat and head coach Sir Ian McGeechan said: "I'm very pleased with our second-half performance.
"We had a poor 20 minutes in the first half when we turned over ball and gave the momentum to Northampton. Winning the second half 10-0 was a good comeback but it was not quite enough, but I couldn't fault our attitude."
Bath, now third-bottom of the table, face a crucial home game against London Irish on New Year's Day, and McGeechan added: "As a group of players they are coming together and we'll see the benefits eventually.
"We have three or four players back from injury in the next few weeks and that will give us greater flexibility and more options."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
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Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
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The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.