The black, green and gold know that a win against the Falcons at cinch Stadium at Franklin's Gardens would secure a top-four spot and a place in the play-off semi-finals on the following Saturday.
It would be a huge achievement for Saints, who had slipped down the standings when they lost to Gloucester on March 5.
Since then, Chris Boyd's side have taken 27 points from a possible 30 in the Gallagher Premiership.
And now they know they need one more big display on June 4 to book their play-off place.
“If it came down to one game at the end of the season, we would back ourselves to go and win it,” Dingwall said.
“Getting two points at Saracens last weekend takes a bit of pressure off us and it's about coming out hot and taking ourselves into a semi-final.
“It's massively important that we send Boydy off on a high because he's done so much for this club.
“He's given opportunities to younger boys, including myself, and there's so many boys who previously may not have been playing but have now gone on to greater things.
“It's massively important to us that we finish the season well and get that top-four spot.”
Saints were 42-17 down at Saracens last Saturday, but they produced a stunning fightback to grab a losing bonus point and a try bonus point in a 42-38 defeat.
However, Dingwall was left slightly disappointed as his side failed to build on a 10-9 half-time lead that was earned despite two first-half yellow cards.
“Overall I'm quite frustrated,” Dingwall said.
“I'll be cheerier as time goes on because we dug out two points.
“The frustration comes from the fact that we battled so hard and got so much out of that first half and then opened the door to them at the start of the second half due to a couple of lapses of concentration.
“Against a top side, like Sarries are, they took their opportunities and suddenly we were kind of out of the game.
“But then we came back and got two points so it's a bit of a weird one to reflect on and it will become clearer as we go on.
“The boys were always aware that, in the league with how tight it is, any bonus point is vital.
“To get one bonus point and then get another, is an added bonus because it means if we win we're in the top four, irrespective of what happens with other teams.
“It's massive that we're still in that top four but the frustration is that we put our game on them when the pressure was off and the game had got away from us.
“We got so much out of that first half and took that one opportunity but it's about coming out for the second half and beating sides like that.
“They are very good at what they do and they do it for long periods. They've been doing it for a long time and they practice it all the time.
“This season has been the first time we've applied pressure and stuck to our game plan for long periods of time.
“We came so close to doing what we wanted but then a 10-minute period pushed it away from us.
“I'll be a lot cheerier about it soon but for now I'm frustrated, which is a positive because we can beat them and should beat them.”