"My immediate emotion was we were back in the game," Anderson told Sky Sports television.
"We were hoping to get the win. Great to have my family here as well and taking over from an English legend is a hugely proud moment for me."
Despite Anderson's record England failed to win as West Indies, chasing an unlikely victory target of 438, finished on 350 for seven to keep the three-match series level at 0-0.
"We got into a great position," Anderson said. "We got ourselves back in the game with great hundreds from Belly (Ian Bell) and Gaz (Gary Ballance) but we couldn't find anything in that pitch whatsoever. We tried our hearts out."
Anderson made his test debut against Zimbabwe in 2003 and has been the mainstay of England's pace attack for the last few years thanks to his ability to swing the ball.
He has 16 five-wicket hauls and has twice taken 10 wickets in a match, his best figures of seven for 43 coming against New Zealand in Nottingham in 2008.
"I think the difference from when I started is that I know my game now," Anderson said.
"When I started I didn't have a clue, ran up and bowled as hard as I could. I developed skills. (The record) has not been a target. I love taking wickets for England.
"My target is to keep my place in the side. We have a hugely talented side at the minute and everyone is very excited about where we go."
Former all-rounder Botham, now a Sky commentator, was gracious after losing his record to Anderson.
"I'm delighted for Jimmy. It's been a burden for him and for me. He was always going past it," Botham said.
"I've watched him develop those skills. It's not easy to bowl the inswinger and away-swinger with very little detail change but it's great to watch those skills. I enjoy watching him bowl, it's a pleasure to commentate."
(Reporting by Ed Osmond, editing by Tony Jimenez)
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