Rhinos are second in the Qualifiers table, two points behind leaders Salford Red Devils who they face at Emerald Headingley on Friday.
The top three after seven rounds will secure a place in Betfred Super League next year with the fourth and fifth-placed sides playing off in the million-pound game.
Rhinos have a two-point gap over Toronto Wolfpack, who are fourth, but Keinhorst insisted: “We have got three games left and we need to target each of them. I don’t think it is done and dusted by any means; we have a massive challenge ahead.”
The tense 16-6 victory two days ago was only Rhinos’ third against top-flight opposition since April, Widnes being the victims each time.
“It’s obviously a relief to get the points,” Keinhorst said. “They threw plenty at us and asked a lot of questions so to come through with the result is a relief and we’ll take that into this week.”
Rhinos have lost a series of close games this year and Keinhorst admitted finally winning one will lift the squad’s confidence.
He was also encouraged by conceding only one try after a run of high scores against them in previous Qualifiers games.
“We showed a bit of character and toughness to keep resilient and keep them out in that second half,” he recalled.
“We had plenty of back-to-back sets against us. We recognised we needed to make some improvements on the previous three performances so hopefully we’ve done that, mostly in our D [defence] and we can take that into next week.”
Keinhorst made a crucial tackle to keep Joe Mellor out in the second half when Rhinos led by four points.
He said: “They asked a lot of questions on our goalline so for us to front up and keep them out says something about us.
“You could sense that desperation in them so to keep them out we had to take it tackle by tackle and focus on the next job each time.
“Fortunately we did enough to keep them out, but it was a tense period.”
Keinhorst, who is expected to join Hull KR – currently sitting third in the Qualifiers table – next year, had a spell on loan at Widnes Vikings earlier in the season.
They look doomed to relegation after 17 successive defeats.
And he said: “I spent a couple of months with those lads so I got to know them.
“Hopefully they can hang in there.
“They are in a tough spot at the moment.
“Whether they can pinch a spot in the last [million pound] game remains to be seen, but I am feeling it for them at the moment, definitely.”
Rhinos’ Richie Myler has received a Rugby Football League caution for dangerous contact in the win over Widnes.
Salford’s Jackson Hastings and Luke Burgess will both miss Friday’s game after being sent-off in their win against Toronto Wolfpack last Saturday.
Jackson was banned for two matches and ex-Rhinos prop Burgess for one.
Rhinos under-19s face Wigan Warriors at Wigan St Jude’s tonight in a game rearranged from last month when it was postponed due to a waterlogged pitch.