While United could be celebrating a Double this season, their old foes Arsenal will end the season empty-handed for the third season in a row.
And Ferdinand said: "This is no time for sentiment, that might sound harsh but I'm sure they wouldn't be worrying about us if we were in a position not to win a trophy.
"We only care about Man United. Arsenal are a great side and play fantastic football but we just need to keep our eyes on ourselves and if we do that we'll go a long way to being successful.
"It's the stage of the season where it's crunch time. The trophies are being handed out soon and the three points today gets us a step closer to being able to pick up one of them.
"Fingers crossed we keep motoring on and playing the way we are doing.
"There's still games we need to win so we have to make sure we get the results that we need and hopefully by the end of the season we'll be the team picking up something.
"But it was a massive result to get three points against one of the teams vying for the title."
United have found themselves pegged back after taking the lead against Arsenal in recent years so Ferdinand was delighted they were able to turn the tables.
And he believes it demonstrates some of the qualities they have picked up in recent years to make them so successful.
He added: "In the past they've managed to peg us back every time we've gone ahead but today was reversed. And when we went into the lead we managed to hold on, so it was nice.
"We showed the confidence and resilience that has been a trademark of ours for the last couple of years. Long may it continue."