The Frenchman thought he had won the game for the Magpies.
The Magpies will head for Old Trafford and a potential meeting with Portuguese superstar Cristiano Ronaldo after the international break with just a single point to their name after three games.
Head coach Steve Bruce faced chants calling for him to go during the eventful 2-2 home draw with Southampton on Saturday, when his side twice allowed leads and a prospect of a first victory of the campaign slip away.
Saint-Maximin told NUFC TV: “We know in the Premier League, the most important thing is to win. But to be honest when you cannot win, it’s better to draw than lose, so we just have to take the positives even if it’s really hard because we have to win this game normally.
“We just have to keep going and to stay together because in the Premier League, it is very hard to not concede a goal – you can see that from the game between Manchester City and Arsenal.
“Every game is really hard and the next game is against Manchester United, so we have to be concentrated and try to do the best things we can do to win this match.”
Saint-Maximin thought he had won Saturday’s game for Newcastle with an added-time strike as they finally roused themselves after an abject first-half display.
The home side had earlier taken the lead through Callum Wilson’s 55th-minute header, although Mohamed Elyounoussi, who scored a Carabao Cup hat-trick at Newport in midweek, levelled with 16 minutes remaining.
Saint-Maximin’s goal looked likely to be decisive until referee Paul Tierney was advised to take a second look at Jamaal Lascelles’ challenge on Adam Armstrong and belatedly pointed to the spot.
It was the third time in as many league games the Magpies have suffered at the hands of the VAR system, although on this occasion they could have few complaints.
James Ward-Prowse’s nerveless penalty secured a point which was the very least his side deserved to leave Newcastle reflecting on what might have been.
Saint-Maximin said: “Sometimes this happens in football. I’d prefer this happens now than in the last three games when it’s maybe difficult for us.”
Southampton boss Ralph Hasenhuttl was pleased to have emerged with a point, but conscious there is room for improvement.
He told the club’s website: “We know we can play good football, but what we should try to do is get something comfortable in these situations.
“It’s important we scored two times today – we’ve scored in every game – but what we are still missing is a clean sheet and conceding fewer goals as this hasn’t changed so far.”