Hughton said: "For me, it was an absolute certain penalty. There are some penalties where you are not sure whether the referee is going to give it or not.
"I could have almost looked away because my first impression was just waiting for the referee to point to the spot."
City boss Gary Johnson admitted his side had perhaps had a lucky escape.
He said: "I must admit, my heart was in my mouth at the time.
"The lads felt there was a bit of contact but from our point of view, maybe he was starting to go down early, we don't know.
"But he [Salisbury] was very brave with forty-odd thousand people screaming for a penalty, anyway."
It proved a hugely frustrating afternoon for the Magpies, who were desperate to bounce back from Wednesday night's 1-1 draw with QPR at St James' Park.
City keeper Dean Gerken produced fine saves with a single second-half minute to keep out Danny Guthrie's close-range volley and Kevin Nolan's header.
However, he needed the help of the woodwork on three occasions to preserve his clean sheet, Harewood hitting the post after seven minutes and Steven Taylor and Nolan both being denied by the crossbar in quick succession with 20 minutes remaining.
Hughton said: "It was very frustrating, but I couldn't fault the manner, in particular in the second half, of our approach to go and win the game against a good Bristol City side who came with a formation which certainly frustrated us.
"But we had opportunities and if we had taken one of those opportunities, I could have seen us going on and getting further goals."
Johnson was delighted with his players, and particularly Gerken, who only discovered he was playing five minutes before kick-off after Adriano Basso picked up a groin injury during the warm-up.
He said: "We made that decision at 2.55pm. I was going to give my super motivational speech and I need them all smiling when I give that and Basso, was grimacing a little bit and doing a stretch on his groin.
"I knew today we needed people to be 100 per cent mentally and physically, and he didn't look either at the time.
"We were able to bring Dean Gerken in and on the day, I would have thought he was a candidate for man of the match."