Plymouth only came for draw, not to win
Brown took over the captaincy from midfielder Matt Oakley, who was banned for one match.
And he was adamant the in-form Foxes were good value for their victory, even though the winning goal came so late on.
"In some games when you are at home and it's 0-0, you are on tenterhooks a little bit at the back because you think the other team might nick one," said Brown.
"But I thought today we weren't in any danger whatsoever.
"I felt very comfortable and credit to the team to restrict Plymouth to probably only one or two shots.
"The lads kept going, showed great character and they kept believing, which is massively important.
"They didn't get disheartened and I personally think we got our just rewards in the end.
"Obviously, Plymouth will think, 'We were unlucky not to get a draw'.
"But, in my mind, they only came here for one reason, and that was to get a draw, not to win the game.
"There was only one team pressing to win the game in the end, and it was us. Thankfully, we got the goal.
"It's not ideal scoring in the 94th minute, but I don't really care about that when we win games.
"It doesn't matter whether it's in the first minute or the 94th minute. A win is a win.
"We have got another three points on the board and we can take a lot of positives out of this game."
Brown almost gave Leicester the lead on the stroke of half-time.
But his close range header was diverted off target by Argyle defender Shane Lowry.
Brown said: "I don't know how it didn't go in. It has hit the lad on the back of the head.
"In all fairness to the lad, he has done well. He has put himself in a great defensive position and it was one that I would have been proud of."
Leicester, the winners of League One last season, moved up to third spot in the Championship after beating Argyle.
But Brown is not getting carried away by their league position at this stage of the campaign.
He said: "It's all well and good being in the top three, but we are coming towards the end of November.
"It's irrelevant at the moment. It's another three points towards the goal we want to achieve."
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