The Magpies rose one point above the 20-time English champions in sixth place courtesy of their impressive 4-0 hammering of Champions League-chasing Tottenham Hotspur in Saturday's lunchtime Premier League kickoff.
Man United could restore the pre-match order when they take on Bournemouth at the Vitality Stadium in the day's evening kickoff, but the earlier result leaves them in a serious battle to finish in the Europa League places this term.
When asked whether Newcastle will finish above Erik ten Hag's side and secure a guaranteed place in Europe's secondary competition this season, Howe told TNT Sports: "Who knows? We've just got to keep doing our bit which is trying to win every game.
"We're hopefully returning to somewhere near our best and we've got to keep heading in that direction."
Ruthless and injury-hit Newcastle produce remarkable result
Newcastle took control of the match against Spurs courtesy of two goals in the space of little over a minute in the first half, with Alexander Isak and Anthony Gordon both netting in the quickfire brace.
Isak doubled his own personal tally in the second half before Fabian Schar capped off a prolific rout which saw Newcastle win by four goals despite only having 27% possession.
It is the second-lowest percentage for a team to win by a four-goal margin or more since records began in the Premier League, after only Everton's 5-1 triumph over Brighton & Hove Albion in May 2023, which they achieved despite seeing just 22.3% of the ball.
The result is all the more remarkable given that Newcastle were without as many as 13 players for the match - the joint-longest list of absentees in the Premier League right now.
Key men such as Nick Pope, Sven Botman, Kieran Trippier, Joelinton, Miguel Almiron, Joe Willock and Callum Wilson are among those on the treatment table, and Howe was full of praise for those who have stepped up amongst his depleted ranks.
"I think the emergence of some of the players people wouldn't have thought would have played will hopefully serve us well for the next few years. Elliott Anderson was excellent, he's been trying to burst into the team and stay in the team," Howe added.
"This season we've really needed [Schar]. he's been the consistent in the team and he's been incredible on the ball. It's no good being on the ball if you're defensively not at the highest level but he has been. His attitude to defending has been excellent and he deserves a lot of credit for his performances.
"Tottenham are unique in what they do and we felt we needed to change to give ourselves the best chance of what we wanted to do. I thought tactically it worked, it was a really good delivery from the players, they always deserve the praise for the execution. Our concentration levels were really good."
Spurs "nowhere near good enough" in heaviest defeat of season
While the result was a significant boost to Newcastle's hopes of playing European football again next season, for Spurs it could prove to be a serious blow to their Champions League chances.
Results by the English teams in European competitions during the week damaged the Premier League's chances of being given five automatic Champions League qualification places next season, meaning that fourth place became all the more important.
Spurs began the day in that coveted position, but ended their match outside it despite rivals Aston Villa not playing, with their goal difference now worse than the Villans' and the two sides still level on points.
Ange Postecoglou's side will now be waiting on a favour from bitter North London rivals Arsenal when they face Villa on Sunday, but the Australian was understandably unhappy with his side's performance en route to their heaviest defeat of the season.
"I thought Newcastle were really good today. We just didn't get to any levels that would allow us to get a grip on the game," he told TNT Sports.
"I thought even before the goals we didn't have a real grip on the game like we usually do. It became a game of transition and we paid the price for that. Even outside the goals I don't think our football was anywhere near the level it should be.
"We'll have time to analyse [what went wrong], right now not really sure."
Micky van de Ven was at fault for the two quickfire goals in the first half, going to ground twice in quick succession to allow Isak and then Gordon clean strikes on goal, but Postecoglou was keen for his players to share the blame.
"I think for all of them that's the life of an elite footballer, you're going to make mistakes. I'm sure he's going to make many more of them in his career. It's about how you react to those mistakes. I think all of us as a group have a fair bit to learn from today," he added.
"It wasn't about the people coming off [when he made a triple substitution], we just weren't taking control of the game, we were allowing Newcastle to dictate. Made the changes hoping we could stem the tide and we did a little bit but it's still nowhere near good enough."
In-form Isak emulates two Alan Shearer feats
Isak's brace means that he now has 17 Premier League goals this season, just two behind Manchester City's Erling Haaland in the Golden Boot race.
Seven of those have now come in his last seven outings for his club, while in the Premier League alone he has now scored in six successive home matches for the Magpies.
The last person to score in more consecutive home league games for Newcastle was their all-time leading scorer Alan Shearer.
However, Isak has some way to go to match that particular run from Shearer, who went on to find the back of the net in each of his first 15 games at home for the club in 1996-97.
The Swede is also the first Newcastle player since Shearer's 28-goal haul two decades ago to reach the 20-goal mark across all competitions in a single top-flight season.