Heart defeated Perth Glory 2-1 in Albury on Sunday, a result which saw them climb to within eight points of the sixth-placed Wellington Phoenix, who they meet at Westpac Stadium next weekend.
Earning a berth in the finals would be close to miraculous following a disastrous start to the 2013-14 campaign, which saw John Aloisi sacked as head coach and replaced by his predecessor on an interim basis.
Van 't Schip did not dismiss Heart's top-six credentials out of hand upon taking control of the team, and the Dutchman is now fighting a losing battle to manage expectations surrounding the resurgent side.
"From the beginning I said everything is possible, but the most important thing is we have to improve our game," he said.
"You can't control other teams, the only thing you can try to control is the way that you play. We're growing, we're getting better, we're getting results. We're coming closer (to the top six). That's important.
"And for us now it's just to continue doing those kind of things. And then we'll see how far we can come and if it's going to be very positive then we'll be very close to getting into a final position.
"But it's far too early to talk about it. I think for us ... the most important thing is try to finish this season in a very good way. That's my first goal."
Heart went behind before rallying to win against both Newcastle and Sydney, managing to beat the Sky Blues despite being down to 10 men, and they responded well to Perth equalising mid-way through the second half at the Lavington Sports Grounds.
"The boys are showing that they are growing in the game plan," van 't Schip said.
"And the results are helping. Not only the results, but also the way we got the results, coming (from) behind. So that creates even more character."
The biggest challenge for both sets of players on Sunday was coping with the intense heat in regional New South Wales.
"It wasn't of course the best circumstance to play a game of football," van 't Schip said.
"It's not a good way to show the people here A-League football."
When asked about Football Federation Australia's decision to delay kick-off by two hours, he said: "I think it was a little bit better, though still unbelievably hot. I think in the end the second half was a little bit better than if it would (have) been played at three o'clock."
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