The Langtree Park supremo hit out after a defeat by Hull KR last month left the out-of-form Saints eighth in Super League and fearing missing the play-offs.
McManus said the team's performance was "nowhere near good enough from a club of the stature of St Helens" and called for a response.
His words may have had the desired effect as - although a top-eight spot is still far from secure - the mood has been transformed in the two games since.
Saints clocked up 40 points as they won at Castleford and then produced one of their best performances of the season to edge out arch-rivals and title favourites Wigan in a derby thriller last week.
Jones, 20, a centre proving himself comfortable in the second row or at loose forward, said: "To be fair, I think he was right in what he said.
"I do think we needed a bit of a wake-up call to start performing.
"We can't just waste a year. We have got a new coach, new facilities. It is massive for us.
"We needed that wake-up call and we have reacted positively to it.
"He (McManus) showed the other night against Wigan how much it meant to him.
"If the club means that much to him we should show the same as he does."
Saints remain seventh in the competition but would leapfrog Catalan Dragons with victory over the French side in Perpignan this weekend.
Given that Leeds have taken the title from a fifth-placed finish in each of the last two years, the Merseysiders - although key man James Roby remains on the sidelines - could be finding form at the right time.
Jones said: "It's a massive game, it should be a great game for the club.
"Beating Wigan was a massive result for us and we can take it forward now into Catalan.
"It's going to be really hot - conditions we like to play in. We're very excited.
"But the win over Wigan will mean nothing if we don't go to France and put a performance in there. We have to keep focused."