The incident came during his final week in charge, Neil walking on to the Riverside Stadium pitch at half-time to speak to referee Oliver Langford about Alan Browne's sending-off.
Browne had been dismissed for kicking out at Sam Morsy in retaliation for the Boro midfielder having twice caught him on the head with his arm.
When the whistle went for half-time, Neil walked quite a distance across the pitch to speak to Mr Langford and his two assistants.
Post-match, Neil insisted he hadn't been abusive towards the officials and had just wanted to make his point about Morsy's actions being missed.
Browne got a three-match suspension for his red card, North End unsuccessful in their attempt to get a slightly lesser punishment.
A statement from the FA released on Wednesday morning said Neil had accepted the standard penalty for a breach of rule E3.
It read: "The former Preston North End FC manager's language and behaviour towards the match referee at half-time of the EFL Championship fixture against Middlesbrough FC on Tuesday, March 16, 2021, amounted to improper conduct."
The 2-0 defeat at Middlesbrough was Neil's penultimate game in charge.
He watched the second half of the match from behind the dug out area, just a few rows back from the technical area.
Neil was sacked by North End on Sunday following the 1-0 defeat to Luton Town at Deepdale.
Frankie McAvoy, who was first-team coach under Neil, has been appointed interim head coach for the rest of the season.
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