Trinity will go four points clear of bottom club Toulouse Olympique if they win at home to Catalans Dragons on Sunday.
Toulouse looked on course to go above Trinity when they led by 10 points at Hull KR on Thursday evening, but two late tries earned the Robins a 22-16 win which boosted their top six hopes and could keep Trinity in the elite competition.
The French side’s final four games include tough trips to Warrington Wolves, Wigan Warriors and Hull FC, as well as a home clash with Catalans.
After Sunday, Trinity have home games against Wigan and Hull KR, plus fixtures at Hull and St Helens.
Toulouse have yet to win on an opponent’s ground this year and Wakefield are now favourites to stay up, but Poching insisted nobody at the club believes the job is done.
“Far from it,” he stressed.
“We have still got a task, we have set ourselves a challenge and there’s some objectives to achieve.
“That is still the same.”
While Toulouse’ form has dipped since they beat Leeds Rhinos three weeks ago, Trinity are improving, having taken St Helens into extra-time before a 32-6 win at Castleford Tigers last weekend.
“The players are working hard for each other,” Poching reflected of what has promoted their better form.
“That was evident in the Saints game, the concentration and effort to execute the game plan was on point from everyone.
“What that builds is trust and belief in each other, that if I perform my role within the plan and do my job in the team I know the guy next to me is going to do it as well.
“That’s where real spirit comes from.
“We are starting to get some of that and we want to carry on with it if we can.”
Poching will select for Sunday from the 17 players on duty last week, plus Kelepi Tanginoa, who was suspended for the win at Castleford, Brad Walker, Isaac Shaw and Kane Evans.
Catalans stand-off Mitchell Pearce could return from the injury which kept him out of last Saturday’s defeat by Leeds Rhinos.
Tom Davies, Tyrone May, Corentin Le Cam, Cesar Rouge and Romain Franco are also in contention for a call up, with Gil Dudson and Joe Chan dropping out.
Poching expects Pearce to play.
“We are working as if he does, but it won’t change our plan if he doesn’t,” he stated.
“If it is Arthur Mourgue who starts in the halves we will treat him with the respect we would Mitchell Pearce.”
Wakefield Trinity: from Miller, Lino, Battye, Hood, Arona, Ashurst, Tanginoa, Crowther, Whitbread, Batchelor, Gaskell, Kershaw, Walker, Aydin, Murphy, Shaw, Hall, Fifita, Evans, Bowden, Shaul.
Catalans Dragons: from Mourgue, Davies, Langi, Whare, Yaha, Pearce, Drinkwater, McIlorum, Da Costa, Jullien, Seguier, Goudemand, Romano, May, Le Cam, Cozza, Rouge, Franco, Kasiano, Tomkins, T Chan.
Referee: Tom Grant (Leeds).
Kick-off: Sunday, 3pm.