Spurs lost all four of their Premier League games in January and suffered a number of new injuries but Postecoglou dismissed the suggestion that he must be frustrated that Danso and Tel were not signed earlier in the window.
"That would be me saying, 'You know, the club didn't really care about our situation, they just twiddled their thumbs until the 29th and then went for it'.
"I know how hard people were working, I don't think people were actively working against me to get what I want done.
"January is generally but this one even more so. All you can ask of people, whether it's players, staff or people I work alongside is that they're doing everything in their power to achieve an outcome. If they're doing that, there's no point getting frustrated, you just have to have faith and trust we'll get the thing done."
Pushed again on whether the centre-half, 26, could have been targeted earlier in the month, he said: "There were certain other things at play for us and for Kevin to be honest.
"As much as you try to understand the pressing need, with all these things there has to be an agreement from three parties. We are not the only ones involved.
"For those three to get aligned and for it to happen really quickly is rare. I mean we got sort of lucky with Toni [Kinsky] because it was their off-season and we could work really quickly there, but most of the other deals got done in the last week.
"Look, it would have been great to get in Kevin early but I am really pleased to get him in.
"He’s a great guy and has already endeared himself to the group in terms of the kind of person he is. We still managed to get a couple of key results in the last couple of games, which really helps our season and now with him in there, it gives us a boost."
"It’s not so much that he rejected us or anyone else. Rightly so he was getting as much information as possible.
"More than anything I think he just wanted to be comfortable with the decision. The sense I get was he didn’t want to be pushed in a certain direction. I think it is credit to him that he took his time and spoke to the right people.
"I had a conversation with him and mine was purely about football. I think he will find a really great place for him in terms of where he is in his career.
"And I think the way we play would suit him and certainly with what we have in the next few months and more importantly what we are building beyond I thought it would be a perfect fit for his next step. At the same time I think it was right to take as long as he did and he was totally comfortable with it."