The win gave England a 2-0 lead in the four-Test series against the side currently ranked number one in the world.
England had to work hard for the win as they recovered from 124-8 on the first day to post a first innings score of 221.
"It was a fantastic fightback and showed a lot of spirit and hunger," Strauss told BBC Test Match Special.
"We've seen quite a few instances of guys standing up when it matters and it's a source of great pride to see."
If England can win the series with India by a margin of two Tests or more they will become the number one ranked Test team in the world.
The Test series resumes with the third match on Wednesday, August 10 at Edgbaston.