Gers fought back from a goal down to lead 2-1, with Arfield grabbing the second goal, but they couldn’t see it out with Hibs finding an equaliser.
Speaking to RangersTV, Arfield said: "It was disappointing and I think everyone watching the game and associated with the club will find it a difficult one to take.
"We have worked so hard to get in front, but you need to see the game out and finish it off, but we never managed to do so and it's hard to take.
"I had my own double chance at the end and should finish the game off and I apologise for that as one of them should go in, but we shouldn't get to that stage I don't think - the game should have been seen out.
"We have to be tougher and more on it if we want to be successful."
Arfield’s goal came following some super play with Ianis Hagi, and he continued: "When we play fluid football, we can open teams up regardless of where we go in Europe or domestically.
"We have good footballers - Ianis sees passes and set me up for one in the first half that was cleared off the line.
"He sees things very quickly and I was glad to get him the assist, but again, it is so difficult to take on an overall basis as this is a game we should have won and moved on."
Arfield has had to be patient and wait for his chance this season, but has now netted in back-to-back league matches for Gers.
He said: "The overall picture is the quality we have got in the team. When we came back from pre-season, the manager kept on adding and players have come back in fantastic form so it is all about being patient.
"The calibre of player has got better and we will add to that, so it is about players being patient and being ready for when your chance comes."
Gers now move on to face Willem II on Thursday in Europa League qualifying, and on that, Arfield added: "That is what happens when you are successful - you have games coming thick and fast and it is what you want - you don't want to wait another week to put it right.”
"Hopefully we can get the right result to stay in the competition as we know how much it means to the fans and the club as a whole.
"This is what attracts players to come and sign for the club and this is another obstacle in our way, but we feel we can go and win the game."
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