Sarries guaranteed themselves a place in the Aviva Premiership play-offs with a hard-fought win.
The defending champions are likely to be away to Leicester in the semi-finals unless results go their way involving Harlequins and they win at home to Exeter.
Gustard said: "If we have to go to Leicester, then we have to go to Leicester. We have a better record than most there, but it's great to get one foot in the semi-final door.
"We still have the chance of a home semi-final if Quins can do us a favour, but what will be will be.
"Our work-rate tonight was terrific and we're really pleased to have won.
"Newcastle are a tough side and they were fighting for their lives, but we defended brilliantly. Our line-out defence was superb and our scrum, which hasn't been at the same level this season, was also superb tonight."
The hosts came close to what would have been a shock victory but, while the losing bonus point kept alive their survival hopes - cutting the gap between themselves and Wasps to just three points - if Wasps win at Bath tomorrow, the Falcons will go down.
Director of rugby Gary Gold will be one of many keeping an eye on the Bath result.
"I don't think I've supported Bath quite as much as I do now!" he said. "On a serious note we asked the guys just to concentrate on what they could do tonight.
"I'm not satisfied with the point but really satisfied with the character we showed.
"I'm devastated with the end result. We prepared to put in a massive performance and get a result and we did put in the massive performance and didn't win.
"All their points came from our scrum. Our set-piece didn't function nearly well enough in the first half at the line-out and in the second half our scrum struggled and we never got anything going from either of those but there was an incredible amount of heart.
"We probably should not have put ourselves under that much pressure to try to win the game in the last few minutes, but we said we'd fight to the bitter end and we did and showed a bit of character tonight."
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