Gaffney saw his side follow up last week's win at Harlequins by making it two wins on the bounce over Christmas after Saracens scored 22 unanswered points after the break.
Tries from Kameli Ratuvou, Cencus Johnston, Glen Jackson and a penalty try saw in-form Sarries snatch their seventh win in their last eight competitive fixtures.
"It has been good - we've had a great Christmas period," he said. "Nine points in two games - I'd have taken that before.
"There was a lack of discipline in the first half - every time we scored we let Northampton back into the game.
"There was some bad box-kicking and we conceded some dumb points. We gifted them a number of points.
"We went out after the break and our discipline was much better in the second half. We set ourselves a goal of being more patient and I also thought we created a lot of opportunities.
"We're confident - we've shown we can compete with the elite. We have more belief in ourselves now but we'll not be over confident, we'll pay respect to sides we play."
Northampton coach Paul Grayson was left to reflect on an injury crisis that has seen the Saints struggle with the hectic Christmas schedule.
Five Carlos Spencer penalties had kept his side in touch at the break, but a below-par showing in the second half saw Northampton wave the white flag.
However, Grayson is now a man on a mission, hell-bent on claiming a second Christmas win with maximum points against struggling Worcester on Monday.
"It disappeared after half-time," fumed Grayson. "We made as many changes as we could at half time - once the game was gone there was no point pushing any of our main players harder.
"We played well but we made some errors. We failed to stop them getting quick ball and they stopped us very effectively.
"Out of three games over Christmas we would want to win both of our home games and that job is half done so far.
"We lost our shape after the break. We were able to kick for territory in the first half and put Sarries under pressure but in the second half we were hanging on as we were going backwards."