The Three Lions were second best throughout the opening 45 minutes at the King Power Stadium, but stayed on level terms until the break and went on to win the match courtesy of Marcus Rashford's second-half strike.
Rose revealed that there were some angry words between the players at the interval and believes that helped them to produce an improved second-half display.
"We could have been two or three nil down at half time. It's great we can all shout at each other and tell each other to improve like we did. In the end, we are over the moon to keep a clean sheet and get back to winning ways," he told BBC Radio 5 live.
"The morale we have set within the squad is fantastic and we have taken off where we left off in the summer. We had a really difficult game against Spain at the weekend, when we were unlucky not to come away with a point.
"Tonight, we have made nine changes and you have to take everything into account. The manager is glad we have dug it out and secured the win."
Rose put in a man-of-the match performance for England, having replaced the injured Luke Shaw in the starting lineup.