The Canaries have been strongly linked with moves for Gary Hooper of Celtic as well as Dutch striker Ricky van Wolfswinkel but Hughton is finding it a challenge.
"We've been endeavouring to do that," said the Norwich boss.
"People on the outside think it's very easy to bring in the players you want. It doesn't work that way.
"If you look at the strikers who've come in you've got to look at the circumstances. That's generally big fees and big salaries.
"These are things that we have to work around. We're still hopeful that come Thursday we'll have some additions."
The task has taken on greater urgency following Saturday's 1-0 defeat in the FA Cup to non-league side Luton - thus becoming the first top-flight team to suffer that fate in the Premier League era.
"The criticism will be harsher from all quarters. It's normal," admitted Hughton.
"We expect all of the criticism that will come our way. We have to be able to take that on the chin. A lot will be made of the fact we didn't win; probably more (than) the fact Luton did win.
"We had the better chances over the game and were the better team. (But) we've got to give them credit. They took the one that mattered.
"Every club will go through this, the ups and downs, it's about how you bounce back."