Despite a statement this week from his representative suggesting he was unsettled, Given produced a number of excellent saves in an entertaining third round tie.
Both sides had numerous opportunities to settle an end-to-end encounter but two stops from Given to deny Daniel Cousin caught the eye.
Hughton, Joe Kinnear's number two, said: "We have got used to that type of performance from him.
"He is a top quality goalkeeper and a top quality individual - but we wouldn't expect anything different from him."
Turner's effort rebounded onto the post and bar off Damien Duff and Given smothered it as it bounced down, with referee Chris Foy ruling it had not crossed the line.
It was an obvious talking point from the game but Hughton felt the decision was correct and Hull boss Phil Brown did not complain.
Hughton said: "I have seen it again, and as per normal you look at the reactions of players.
"Their players are always going to see it going over the line and ours could see it for what is was, hit the crossbar, went into Shay Given's hands and certainly not over the line."