The Cobblers, beaten play-off finalists under Boothroyd in May, were brushed aside 3-0 at Mansfield on Saturday and have picked up just four points from a possible 24 in League Two this term as well as exited two cup competitions.
But Boothroyd told BBC Radio Northampton: "The club is in a far better place than it was and it's only a matter of time (before results improve).
"I'm not one for resigning or giving up. These are my players. I've got backing from everyone within the club. I'm the man to put this right."
He added: "I've got a pretty good track record, not just here but elsewhere.
"I'm not shirking away from anything. I was the man to put it right when we were bottom of the league before.
"Whilst it irritates my ego to be asked the question (about his position), you're right to ask it and so are the supporters. But true supporters know what's going on.
"We live in a society where we expect quick fixes. I fixed it here quickly and now we're going through a different period of our development."
Boothroyd took over at Sixfields in November 2011 with the Cobblers three points above the drop zone in League Two.