Many Spurs fans may be feeling as though the Europa League is their best chance of salvaging Champions League qualification for next term.
However, Postecoglou spoke after a 2-2 draw with Wolves on Sunday, stating they can still push up in the league.
He stated: “I think so. Because it's still fairly tight. I just feel that at some point we'll get a relatively healthy squad and when we do that we'll be able to perform at a high level consistently and we've already shown this year we can beat anyone.
“There's a chance there you can go on a run. But at the moment that's secondary to the first bit, we have to try to get some support for the players - both mentally and physically and in terms of numbers to give them the opportunity to play at their best.”
On the reaction to letting in a lat equalizer against Wolves, he added: “Of course I am. It hurts me because I'm responsible ultimately. I'm the person in charge. So of course it hurts.
“When I see how hard they are trying, it hurts even more because you want them to get a reward and I think today they deserved a reward for their efforts even though they were dipping into their reserves of energy, which I don't even know where they got from.
“I wanted them to get a reward for their efforts. So of course it hurts. It hurts immensely. At the same time it's my responsibility for where we're at right now and it's my responsibility to try to get us out of it.”