Hawley, who signed for the club on Friday, was brought on for his debut 55 minutes into the game alongside fellow new-boy Leon Clarke, and believes the Iron should have claimed the win against the Blades.
Hawley told The Iron Player: “We’re obviously disappointed not to take all three points, but we have got to look at the positives and we did get a point.
“All the boys are disappointed because we knew this was the perfect opportunity to get the win, but things didn’t go our way towards the end and that is football."
Leon Clarke came on to score the Iron’s only goal, and Hawley believes that the ex-Sheffield Wednesday striker had an impact on the game.
“Leon got off the mark straight away, which is brilliant for him and it looked like he was going to win us the game," added the 30-year-old.
“The team played well and it is difficult against nine men but it does sound easy to play 11 v nine.”
The former Notts County frontman admitted Danny Wilson’s side made it difficult for the Iron to break down the visitors.
“They just sat back and made us try and break them down, which we tried," stated the striker.
"They then they got the breakthrough from the free kick, which personally I didn’t think was.
“The boys played well and we should have got the three points but we have just got to pick our heads up and go again next week."
United had the majority of possession against their Yorkshire counterparts, but were unable to score more than the one goal to kill the tie off, and this is what the ex-Carlisle frontman believes cost the side.
“I don’t know how much possession we had of the ball, but when we have so much of the ball, you need to be taking all three points," he insisted.
“Some of the referee's decisions were dubious, but I think he got the two sending offs correct.
"There was no doubt that they were red cards, but I am just going to leave the referee to do his job.”
He continued: “We play Shrewsbury next Saturday, we will be working towards that all week and we will go down there full of confidence and off the mark, which is a stepping stone.”
See much more from Karl Hawley, Leon Clarke and Alan Knill on The Iron Player.