Solskjaer was handed a three-year contract last week after a successful spell as interim boss since December.
The former United striker's astute leadership has revived a club in turmoil during his predecessor Jose Mourinho's reign.
Fan favourite Solskjaer has led United into the Premier League's top four and the Champions League quarter-finals.
There was a celebratory atmosphere ahead of Watford's visit to Old Trafford on Saturday. Then Marcus Rashford and Anthony Martial goals sealed a narrow 2-1 win.
Solskjaer knows it was a "sloppy" display and Jones accepts it was far from United's best, but the long-serving defender is excited for the future and loving life under the Norwegian.
"The lads are buzzing. He's come in, he's been a breath of fresh air for us. He's put arms around the shoulders of people who needed it," Jones said.
"His man management skills are terrific and he's definitely what we need going forward. Everyone can see that he has laid foundations.
"The fans, the media, everyone can see what he's done and how he wants to play since he has come, and we've shown that in quite a few games.
"It's positive, we're looking forward and we're pleased with the result."
With a remarkable 35 points since Solskjaer's arrival from Molde, United are the Premier League's form-team even though the title remains out of reach for this season at least.
Asked what United's blistering run will do for their trophy chances in the Solskjaer era, Jones said: "I don't think we're far away.
"Obviously we had a poor start to the season. It's sort of like a story of two halves of the season, really.
"He's come in and done a terrific job. I'm delighted he's here now and we can move forward and progress under him.
"That's the vision for the players, the staff, the fans, everyone involved in this football club, to win trophies.
"It's a wonderful place to play football and that's where we want to get back to."