The England defender delivered the bombshell claim ahead of tomorrow’s Champions League last-16 first-leg clash at home to Paris Saint-Germain.
United have taken 25 points out of a 27 under interim boss Ole Gunnar Solskjaer.
And Jones said: "Everyone’s going to take us seriously now.
"We might have been a bit of a laughing stock at the start of the season — but certainly not now.
"We’re improving, still getting better.
"It was tough for everyone involved. Everyone at the club, the supporters, everyone.
"But it’s about becoming stronger and seeing that through. I’ve said in the past, we’ve not achieved anything yet.
"We’re under no illusions of that, but we’re heading in the right direction."
Before Mourinho was sacked in December, United struggled under the Portuguese boss both with the results and style of play.
Jones, whose team beat Fulham 3-0 on Saturday, added: "There is a positivity about the place to grind results out when we’re not playing well.
"To play forward, to play with intent and purpose and that’s exactly what we’re going.
"You can see it in every game. We’re creating a number of chances and putting them away.
"Consistency is the key in every sport. We’re putting a run together and we need to keep that momentum going and keep picking up points."
Jones, 26, also gave an honest answer when asked about the announcement of his new four-year contract which was criticised by some fans.
He added: "Listen, I don’t lose sleep over what people say about me.
"It’s football. I’m going to get criticism in the future, I’m going to get criticism in the past. I generally don’t care.
"I have a wonderful family, wonderful friends and I play football for Man United.
"I’ve been given an extra contract and I’m thankful and grateful for that. It’s great."
United now have a run of tough games starting with Tuesday's visit of French giants PSG.
Jones said: "Football can change very quickly and I know that. I’ve experienced that numerous times.
"One minute you can be up there, the next you can be down there. It can change very quickly.
"It’s a cliche, but feet on the ground, one step at a time and we’ll look forward to PSG on Tuesday night."
Two-goal Paul Pogba, meanwhile, also appeared to deliver a dig at former boss Mourinho by insisting Solskjaer was not "acting".
Asked about Solskjaer’s secret to success, Pogba said: "It is his joy. He is just being himself.
“He is not playing acting.
"He is being himself. He is giving joy to everyone.
"He is giving confidence to everyone — and you can see on the pitch."
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