The County dominated proceedings throughout the contest and were the only side capable of winning going into the fourth and final day.
But a staunch rearguard action from the hosts, who batted out the day, and five full sessions in all, to end on 328 for nine in their second innings having been asked to follow on, and that saw them 135 runs ahead of Northants' first innings total of 390.
Paul Walter hit an excellent 93 over five and a half hours while Adam Wheater used up 174 balls for his 33 not out.
For Northants, Rob Keogh - in his 100th first-class appearance for the club - claimed four for 51, which included his 100th wicket as well, while Tom Taylor took three for 62.
It was a frustrating end to the four-day clash for Northants, but Vasconcelos was proud of the efforts of his players.
“Things didn’t quite go our way either Saturday or Sunday, but you can’t fault the effort everyone put in out there for 220-plus overs," said the skipper.
"Not once did we look as if we went flat. We kept running in, hitting the pitch hard the whole time. Unfortunately, we just didn’t quite get there.
“The pitch did flatten out on days three and four.
"The sun that was out on Saturday and coupled with the heavy roller on it made it a bit dead, but that’s how it goes sometimes.
"We tried everything, different plans here and there. We tried pretty much all of our bowlers. So I’m gutted we couldn’t get over the line, but we played all the cricket this week.”
The result means Northants are unbeaten after three Championship matches on their return to division one after an eight-year absence.
The County are in sixth place in the 10-team table on 38 points, but are only eight ahead of bottom-of-the-table Kent, who have played a game more.
Next up for Northants is a trip to leaders Surrey, who are also unbeaten and have garnered 67 points from their four matches to date.
They drew a high-scoring clash at Gloucestershire over the weekend, with the home side making 443 for two in reply to Surrey's mammoth 603 all out, with Jamie Smith hitting a career-best 234 not out and Jordan Clark 137.
Sunday's final day was a washout.
Vasconcelos and his team head to the Kia Oval on Thursday (11am start).
Essex v Northants match facts: Northants 390 all out (Luke Procter 113, Gareth Berg 75, Will Young 63) drew with Essex 193 all out (Ben Sanderson 4-32, Matt Kelly 2-50) & 328-9 (Rob Keogh 4-51, Tom Taylor 3-62)