Despite struggling to find assistance from the batsman-friendly Newlands pitch, the tourists’ attack stuck to their task admirably and created a couple of chances that they failed to take.
Amla was given two lives, on 76 and 120 respectively, when Anderson and Nick Compton were guilty of spilling opportunities.
But with South Africa managing only 212 runs in 87 overs today, leaving them 276 adrift on 353 for three, Finn was pleased with the bowling efforts.
“I thought we never let them get away from us, we created pressure, those little chances. Unfortunately we didn’t take them,” he told Sky Sports.
“It’s been a long hard slog but I think everyone has put a lot of effort in and I don’t think we can fault the way we bowled at all.
“If you look at the way people have got out this game, there has been one person who has been nicked off – Alex Hales – everyone else has contributed to their own downfalls.
“As a bowler you need to mix it up as much as you can. If there is no swing or sideways movement you have to change your pace, change your length and play with the batsmen with your field changes. I think we did that really well today, we just didn’t get the rewards.”
The 27-year-old, with three first-class wickets to his name, seemed to unsettle the batsmen with three overs of his gentle off-spin.
— Graeme Swann (@Swannyg66) January 4, 2016
And Finn joked: “We opened the bowling for Hertfordshire Under-12s and that is the first time I have seen him bowl for 14 years. I don’t wish to see that again!
“It is funny because sometimes with that sort of bowling the opposition can be scared to play a shot almost and you can sneak a wicket and that gets you a breakthrough. Then your main bowlers can come on.
“Hopefully we never get to a situation when we see Alex Hales bowl again! But if it brings a wicket then that will be great.”
With the pitch not offering assistance, England knew they would have to take their chances when they arrived.
Anderson and Compton joined Joe Root in shelling catches, the Yorkshireman putting De Villiers down on five last night, while Finn saw a Du Plessis leading edge drop just short of him at mid-off.
He believes the setting of Newlands, a beautiful ground overlooked by Table Mountain, makes it difficult to pick up the ball.
“It is very difficult to see, even the one that dropped short to me at mid-off I didn’t pick it up until it was half way towards me,” he said.
“It is tricky to see here and sometimes people drop catches, that happens in cricket, we have been excellent at taking catches this series so far and through the summer as well. Hopefully tomorrow we can take those catches.”
Only nine wickets have fallen in the first three days, making a draw appear the likely outcome, but South Africa are still way behind England’s 629 for six declared and Finn still holds hope that they can make further in-roads tomorrow.
“I think we are a long way ahead in the game,” he added. “It is going to take a lot of hard work, as we have seen today. We have got one wicket and we bowled pretty well.
“We are going to have to come back tomorrow and really put some pressure on South Africa, even more pressure than we did today, and that is a challenge for us as bowlers to try and create those chances.
“We are still pretty upbeat and chipper in the dressing room. Yes, we have had a tough day, but we are a long way ahead and we try and force something tomorrow.”