Victory was Westley's first in nine League One games following a miserable run that has seen them drop down the table. But his captain John Mousinho scored the only goal in first-half stoppage time to ease the pressure on him.
"Three points is always valuable and with big players out and results not going our way it's a positive to get that winning vibe back to the club," said Westley.
"The response to the weekend was good. We try to change the team around a bit because they work hard over Christmas and there is the added family pressure as well on top.
"A clean sheet pleases me, I place value on defensive displays and being dogged. You want to see that workrate in blustery conditions and sometimes you have to rely on that to see you through. It needed a lot of defensive resilience to see it out."
Mousinho's goal came from a deep corner from Jack King and the skipper found space to head across goal and through the legs of goalkeeper Scott Flinders.
Pools, bottom of the table with only two victories all season, won at Sheffield United at the weekend but were unable to build on that shock triumph.
The Lillywhites were thumped 3-0 by Doncaster on Saturday and Westley admitted: "We knew we needed to bounce back. Hartlepool won at Sheffield United and were never going to be easy opposition - they would take confidence from the weekend and we knew we had to knuckle down.
"We scored from a set-piece and got a penalty - and there was shock waves going through the club as a result.
"In the second half we were organised, hard-working and tough to break down - everything you need to be in this situation we have been in. It was backs to the wall with good counter attacking in the second-half."