The Hull head coach is trying to keep his squad grounded despite being just four points off the play-offs following a ninth game unbeaten in the league.
Adkins is also hoping to ward off interest in in-form winger Jarrod Bowen after his double set up the win against Wednesday.
Bowen has reportedly attracted interest from Premier League duo Tottenham and Leicester but Adkins is keen the player achieves more with the Tigers.
Adkins said: “We’ve highlighted to the players it’s the next game and it’s the performance in the next game (that’s important).
“If we can drive our performance level we can give ourselves an opportunity (of reaching the play-offs).”
Adkins prefers to concentrate on preventing a return to the poor form which saw Hull in the relegation picture earlier in the season.
He said: “We’ve still got to achieve our first objective.
“We are on a real good run of form. That’s six league wins on the spin now. The last three league games have been clean sheets.
“I thought it was an excellent display, we totally dominated the game. I thought we were good value for the victory. We have got to keep driving our performance.”
On the interest in Bowen, Adkins added: “We want Jarrod to go to the highest level he can, we want all of the players to go to the highest level they can.
“The owners have said we will not be selling our best players.”
Bowen added to his growing reputation as he struck in first-half stoppage time and converted from the penalty spot shortly after the break, before substitute Fraizer Campbell underlined the home side’s superiority in the last 10 minutes with the third goal.
Without several fine saves from Wednesday keeper Keiren Westwood in the first half the margin of defeat would have been much heavier.
The keeper kept out two shots from Kamil Grosicki and a Chris Martin effort before the break as a George Boyd shot was all the visitors had to show and threatened even less after half-time.
Wednesday caretaker manager Steve Agnew admitted the better side had won.
He said: “It was a disappointing result and a bitterly disappointing performance. From the first minute Keiren Westwood made a terrific save and that kind of continued all afternoon.
“The third goal killed it off. We were never in the game and never showed any desire and Hull thoroughly deserved the win.”
Agnew has been put in charge alongside Stephen Clemence until new manager Steve Bruce takes over next month.
Agnew added on the performance against Hull: “It does tell us things about the players and they have to understand what we require. What we have found is they are a decent group of players.
“It’s one of those afternoons whether I was sat here or Steve Bruce was sat here we would have been saying the same things.”