Neil raised the subject in his post-match press conference following the 1-1 draw on Saturday which was a seventh game unbeaten for North End.
Browne was recalled to the starting XI after being on the bench against Sheffield United the week before, playing in the No.10 role behind Jordan Hugill.
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The Irishman later gave way to substitute Josh Harrop in the second half.
Neil said: "I thought the game last week against Sheffield United suited Daniel Johnson, while I thought on Saturday we needed a running midfielder to go beyond Jordan which we did with Alan.
"That is something I'd like to bring up, it frustrates me when I hear some people in the stand moaning and groaning at Alan or any of our players.
"They are honest lads, work their nuts off for this club and Alan has been fantastic for us this season.
"Then you heard some groans which frustrates me,for what that lad puts in he deserves to be supported by our supporters."
Asked specifically about what he had heard, Neil said: "I just felt within the game there a wee bit of edginess, if he made a bad pass people would start groaning at him.
"That really frustrates me because Alan does so much hard work.
"If you look at Alan's stats in terms of running - people say we are playing football, not running - but you need to run to play football.
"The fact is Alan is in the team to give us energy, give us legs to stretch teams, to get in behind them, to make good diagonal runs to get up to support Jordan - he does all that.
"The next bit he needs to add to his game are goals and we are fully aware of that.
"He is trying really hard to do that.
"If someone is not trying hard and fans are giving them stick, I'm all for that because I would be giving them stick as well - I've no issues with that.
"But when players are trying as hard as they possibly can for the team, for themselves, for everyone else, I think they deserve a bit of support.
"I might be talking out of a bit of frustration at the moment but that is fine, I can live with that.
"I'm a big fan of Alan Browne, I think he does a lot of hard work for us."