The pair, who play mother and daughter Charity Sharma and Debbie Dingle, were among the 61 cast members who took part in the special 40th anniversary broadcast.
> 'Emmerdale's 40th anniversary - full coverage
Charity was at Debbie's side yesterday evening (October 17) as she gave birth to a baby boy in big scenes for the Dingles.
Speaking afterwards on ITV2's Emmerdale Live: The Fallout, Atkins confessed that she found herself thinking about the viewing audience while playing the scenes.
Atkins commented: "I think the pressure is immense. I mean, we've loved it, but there's so many emotions. You can't imagine what it's like. It's unbelievable.
"Your head can go to, 'There's 10 million people watching this', and it's just a natural thing where the human brain can go. I think a couple of times it went there! That's probably part of it, part of the thrill - but it's bloody scary!"
Webb added: "It's really difficult, because when you're in it… the pressure really got to us. All I was thinking all the way through was, 'I can't do it'. Even when I was doing the dialogue, it was so hard."
Emmerdale Live pulled in an average audience of 8.8m, and the show's cast appear to have covered up their nerves well as fans have praised their performances in the special.
The aftermath plays out tonight (October 18) at 7pm and 8pm on ITV1.