Ulster boss Mark Anscombe has tipped Saints to bounce back with a big show in Belfast on Saturday.
And he has warned his players not to get too carried away with their stunning 25-6 success at Franklin’s Gardens on Friday night.
Ulster were outstanding as they scored four tries and kept Saints out in a dominant display in the pool four showdown.
It means the Irish side are now eight points ahead of Jim Mallinder’s men in the race for the knockout stages.
But Anscombe says the win at Saints will mean nothing should his side surrender on their own turf in the coming weekend.
“It’s a bit of a statement to say ‘we’re here and we’re in it’, but we’re certainly not getting carried away,” he said.
“We’re by no means looking too far ahead. They’ll be smarting from that performance and they’ve got too many quality players not to bounce back.
“Even though it’s at home next week, we’ve got to keep our feet on the ground and make sure we bounce back from this performance and go out and do it again, otherwise this counts for nothing.
“We’ve got to do that again and then we’ll be in a pretty good position to qualify out of our pool and that’s the key, but we’ve still got three games to go.”
While their backs were ruthless, Ulster’s forward pack, including former Saints No.8 Roger Wilson, more than matched their English opponents.
And Anscombe paid tribute to the effort of his big guns, who fired to ensure their team stayed on top throughout the game.
“We knew we had to combat their forward pack at scrum time and lineout and I thought we did a pretty good job of that,” he said.
“We used the ball we got and scored some good tries so it was a dominant performance overall.”