They are in contention to qualify for the next round of the Europa League and play Tamworth in the third round of the FA Cup on January 12.
“It’s not like our schedule is going to get easier at any point. So I think it makes sense. We’ll try and strengthen,” Postecoglou added.
“You just don’t want to panic and bring somebody in, which you don’t think will help our cause in the latter half of the year, but I think we’ve already shown that we’re quite methodical and prudent about our work.”
Postecoglou has faced questions over Spurs’ recent Premier League results and his tactics, but he refuses to blame his players.
He added: “They’re giving absolute maximum effort and what they’re doing is backed up by the physical parameters you put against it. They’re trying to do it the way I tell them. So how can I be? Criticize it?”
Postecoglou also defended his reaction last week, where he accused the Match of the Day reporter of discounting the impact of Tottenham’s defensive injuries after the defeat to Liverpool.
“I wasn’t angry, but I don’t know many managers who bounce into interviews after a defeat and are all ecstatic,” he said.
“To be fair I’m getting tired of the same questions over and over again, and maybe it’s easier to get a response after a defeat.”
