The Premier League champions have made an indifferent start to the season under new boss David Moyes, but a 1-0 victory over Arsenal on Sunday dragged them back into the title race.
Moyes faces the unenviable task of following Alex Ferguson, after the Scot brought his trophy-laden tenure to an end when retiring at the end of the last campaign.
"People want us to fail because we have won the league so many times," he told the Guardian. "United won the league long before I was here. Everyone hates the best clubs, it is as simple as that.
"We enjoy that. We relish the test we get thrown at us week in, week out."
Jones also believes United's victory over Arsenal has put them in a perfect position to start climbing the Premier League table.
"It (the victory over Arsenal) 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," he added.
"We weren't champions for nothing. This is a step in the right direction going into a busy period."
