Heather Knight put on a true captain's display as her half century helped England chase down India's below-par total of 134.
Having lost the opening three matches of the tournament, England needed a win to maintain their hopes of defending their title.
Speaking after the match, Shrubsole said: "There was no discussion about how quickly we wanted to chase it down. We've obviously lost our first three games, so it's all about getting over the line.
"I think the way that Heather batted to see us there, I don't think I need to go into how we chased it… we chased it and I think that's all that really matters."
England eradicated fielding mistakes which led to their three defeats against Australia, South Africa and the West Indies.
Shrubsole believes the performance against India was a good step forward for her side saying: "We're going to have to do all the same things before the next game and not take things for granted, but I think fielding can often be a confidence thing.
"I think that's much closer to where we're at as a team.
"We haven't shied away from the fact that we've been really poor in the field in the first three games, the last two in particular, and it's good to put some of that right today and hopefully it's a step in the right direction for us moving forwards."
One of the stars of the shows against India was 21-year-old Charlie Dean whose bowling figures of four for 23 earned plaudits from her teammates.
"I'm absolutely buzzing for Charlie," added Shrubsole. "Obviously this is her first World Cup, to come in and bowl as well as she did in what was a really high-pressure game… I'm over the moon for Deano.
"She's someone who's really popular around this group and is an immensely talented cricketer and hopefully she'll be taking wickets for England in World Cups for years to come."
Next up for England is another must-win encounter against the tournament hosts, New Zealand.