The Reds are aiming to improve on last season, when they went trophyless, as they started their Champions League group stage campaign.
Despite a tremendous effort from Milan to take something from the game, Henderson's second half goal helped the home side to a 3-2 win at Anfield on Wednesday night.
Asked about their character, Henderson told the club website post-game: "Very important. First game, you want to take three points and get on them on the board early, especially at home, so we've got to be really pleased with that.
"But again, I think the performance level for 70-75 minutes was very good and we just need to learn about that 10-15-minute spell and make sure that doesn't happen too often otherwise you'll get punished at this level.
When asked if they made life hard for themselves going 2-1 down, after having been 1-0 up, he added:
"Yeah, we made hard work of the game but you've got to give credit to Milan.
"They're a good side, good players, and when you're not quite at it in a spell in a game, you get punished at this level and they did that.
"But I thought the boys reacted so well in the second half… we kept going, kept fighting and managed to find a couple of goals to win the game, so overall delighted with the result."
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