The Three Lions earned a dramatic 14-run victory over the Aussies at Trent Bridge to take a 1-0 lead in the tour.
"It's been a great Test match, a very even Test match and I don't think I've played in one in which the momentum has changed so quickly, so often," Cook told reporters. "I'm glad we managed to scrape through at the end. We've obviously had little nightmares over their last-wicket stands in both innings.
"In the heat of the moment you can panic but you have to look at conditions and with a reverse swinging ball, you just felt we would give ourselves some chances to take. Everyone is heightened. You are going to be nervous. But sitting back now that's why you play the game. The atmosphere after lunch was incredible.
"Now it's a job for our backroom staff and for us as a team to make sure we recover well from this because back to back Test matches are hard physically. We have to come back on Thursday ready. Clearly Australia are going to be disappointed, like we would have been, but it's all set up nicely now for Lord's."
The second Test takes place at Lord's from Thursday.