Home boss Mick McCarthy felt his side were about to get a point but wasn't happy about the way his team conceded the goal.
"I don't think the 'keepers have really had too many saves to make at either end and it looked a goalless draw all over," he said after the game.
"It was a goal out of nothing. We gave the ball away from the throw and then blinked for a second and Arfield has made the run and got his header in. It was little mistakes that cost us. if we had defended better for that one moment, we would have got something from the game.
"I'm please enough with the performance. We had the better of the chances in the first half but give them credit, they defended really well. They are scoring goals and if they are defending like that, that's why they are top of the league.
"I don't think there is much between the two teams but it's just little mistakes in games that are costing us."
Sean Dyche saw his side win yet again and said: "All credit to everyone. The players put so much effort into that performance again today and although there were quiet moments in our display, we still found the wherewithal to go and win it 1-0.
"Within all that I am really pleased that we have turned around what could have been a negative situation. There were people questioning why we sold Charlie and then about the funds and all of that, so I am so pleased.
"The board came out and were very honest and we came out and said we were believers in the people we work with. So I am really pleased for the players and the supporters who looked beyond that.
"Of course, results galvanise it all, but I just feel there is a positive energy and feel about the group and the idea of all noses pointing in the one direction.
"I always say that results cement all that, and if a couple don't go our way that is when we really need to show there are no cracks and no asking questions, but in the meantime that is another fantastic win at a tough place to come."
He added: "It's all about mindsets. I told the players on Thursday they were going to hear all the messages about 'we never win at Ipswich', but it's a load of old nonsense. What happened ten years ago cannot affect a performance here today.
"It's impossible so we just go out there and go hard with everything we've got when the whistle blows and I am pleased to say we did that.
"Mick's team are hard to play against here, where they have a good home record. I thought they edged the first half and our basics kept us in it. In the second half it calmed a bit and we looked like we were beginning to find that fluidity and, in a game where most probably thought it was heading for a draw, Scotty popped up to win it."