Henderson struck his first goal of the season to earn all three points at Anfield on Saturday as Liverpool moved into sixth place in the Premier League.
Having combined with Adam Lallana for the opening goal, the 24-year-old slid home the winner on 61 minutes after good work from Raheem Sterling inside the penalty area.
Rodgers was delighted to see the England midfielder cap an impressive performance with the decisive goal, citing the former Sunderland man's newfound freedom to break on as crucial.
"We gave him more licence [to get forward]," Rodgers said.
"He's the one player in the country who can dominate the game without the football with his running capacity, his great physicality and today was about getting him forward that bit more.
"That running allows him to offer the combination with Adam for the first goal and the second he arrives in the box and finishes really, really well. It was a big performance from him today.
"He has wonderful physical capacity to run. His size surprises a lot of people, he's got great running ability [and] lovely technique on the ball."
The Anfield manager admitted there were still improvements needed from his side over the coming weeks, but expressed encouragement at their determination to come back and seal victory.
"Performance wise we've still got a way to go," he added. "The speed of our game, movement in our game [and] intensity in our game is still developing and improving.
"I'd rather have that now and get better and better as the season goes on, but whilst searching it is important to find a way to win.
"The players have got remarkable character. It was a very important win for us today, hopefully we'll come back from the international break to what we were at Tottenham with a full squad to pick from."
