But there was no hiding Sale's slackness in defence, with Sarries - who had three men sin-binned - grabbing tries through Rodd Penney, Ben Johnston and Glen Jackson to keep the scoreline close until the final whistle.
The champions have yet to find the form of their title-winning campaign of last season, and Saint-Andre was not impressed with the performance in this latest victory.
"I am pleased with the win and that Saracens did not get a bonus point," said the Frenchman. "But I think they deserved something.
"We were okay going forward for 50 to 55 minutes but after that we switched off completely. "We started to be individual. We looked shaky in defence and we need to be much better, and improve together.
"We were 12 points in front, but although we were 15 against 14, we did not close the game out."
Saracens director of rugby Alan Gaffney admitted ill-discipline was his side's downfall as the Londoners slipped to their second defeat in four league games.
The visitors' sin-binnings, which occurred just before and just after the interval, cost them dearly as Sale forged into a 26-9 lead.
Three tries in 15 minutes brought Sarries back into it, but they could not do enough to bridge the gap.
"We dug in, but our ill-discipline let us down again," said Gaffney.
"We gave away too many penalties - the penalty count in the first half was 11-3 - and we just had no ball.
"Three guys getting binned does put a bit of pressure on you.
"That obviously changed in the second half when we had a crack at them. We played a lot better then."