The England international believes the Red Devils proved they are more than capable of retaining their title by defeating the Gunners at Old Trafford.
David Moyes' men risked falling 11 points behind the Gunners had they lost at Old Trafford, but the hosts claimed victory thanks to Robin van Persie's 27th-minute header to move up to fifth place.
Jones is adamant the win is a sign that United remains a force to be reckoned with in this season's title race and hopes to use the victory as a springboard after an otherwise unspectacular start to the season.
"It proves when people doubt us, we are more than capable of standing up for ourselves and proving to
people that is why we were champions last season," the versatile 21-year-old told to PA Sport. "We weren't champions for nothing. We thoroughly deserved all the points we got last season. This is a step in the right direction going into a busy period."
The player said he feeds off of the negativity many direct toward the Premier League champions.
"People want us to fail because we have won the league so many times. United won the league long before I was here," he said. "Everyone hates the best clubs - it is as simple as that. We enjoy that and relish the test we get thrown at us week in, week out."
Jones, who began the match in central midfield before moving to center back following injury to Nemanja Vidic, was full of praise for his side's attitude against Arsenal and says United fully merited the victory.
"Everyone put in a shift and dug deep," he added. "We thoroughly deserved the three points. The boss set us up in a certain shape all week. He went round individual players and prepared us really well. It has shown that has worked. It was one of those games, no matter where you play, it was just a great game to be involved in. It was a feisty affair with tackles flying in and the crowd were up on their feet.
"When you get a win like that, it just makes it ever so sweet."