In a rather bizarre season, where most teams have struggled for consistency at times, Everton remain the only Barclays Premier League outfit to have just once.
Although some of their results have not been that convincing, a tepid goalless draw at Crystal Palace springs to mind, they had managed to clamber up to the fringes of a top four berth ahead of Wednesday's trip to Old Trafford.
With an equally testing away day to come at Arsenal on Sunday, it represented the acid test of Everton's credentials.
But with Bryan Oviedo's late goal earning the Merseyside outfit their first Old Trafford triumph since 1992, Coleman feels Everton have served notice of their intentions.
"I hope people start taking us seriously now," said the Republic of Ireland international.
"We have a very good team and a great bunch of lads.
"If we can go to Manchester United and win we can go anywhere and do it.
"That is what the manager has been telling us all season, not to be afraid of anyone."
As Oviedo revealed, it was a point manager Roberto Martinez reinforced in the build-up to the game.
"The manager got us together and asked us what we wanted from this game," said the Costa Rica international.
"He said it was very important because it was a chance to show we should be at the top of the league."
That Everton deserved their success just made the victory even sweeter.
Although United did have chances, striking the woodwork twice, and the visitors were indebted to former Red Devils keeper Tim Howard for a brilliant reaction save to deny Patrice Evra, Martinez's side were the dominant force in midfield.
The mobility of Ross Barkley and James McCarthy was in stark contrast to the lack of movement from United, for whom Marouane Fellaini continues to be a major disappointment.
And with Gareth Barry anchoring, Everton were able to keep their hosts at bay for long periods.
Still, it was a contest that appeared destined to end goalless until makeshift full-back Antonio Valencia failed to react as Romelu Lukaku's mis-hit shot flew across goal, allowing an unmarked Oviedo to fire home from close range.
Filling in at left-back for the injured - and possibly United-bound - Leighton Baines, Oviedo has now scored in successive games, having opened his account for the club in their win over Stoke last weekend.
"This has been my best week in football," he said.
"To score two important goals in one week is very good for me. It is a bit of history for us and a very good night."
But the job is only half done.
A wounded United is one thing, an Arsenal side in top form and looking like genuine title contenders for the first time in years is quite another.
"We knew we had two very difficult away games," said Oviedo.
"This one is finished. We have won. That is very good for us.
"Now we play one of the hardest games of the season. To play at Arsenal away from home is very difficult."
Source: PA
Source: PA