The 20-year-old defender had been booked in the first half for deliberate handball and was sent off when he was given a second yellow card for a challenge from behind on Eddie Johnson in the 61st minute.
Mark Rivers had given Crewe a 30th-minute lead that had been cancelled out by Morten Bisgaard just after the break and the visitors looked the more likely to record victory until Davies saw red.
Brown was unsure whether he could appeal against the decision - he was unsuccessful in his attempts to get Richard Jackson's dismissal in the 2-1 defeat by Watford overturned - but revealed he would do everything he could to avoid Davies being suspended.
"We looked like going on to win the game and we've had a major incident go against us, and wrongly so, again," the Rams boss said.
"I've had a look at it three times on the replay and Andy Davies got the ball. I know he got himself into trouble in the first half with a stupid handball, but the incident that he got sent off with, the referee has got it wrong. He's got to look at it on its merits and (Davies) tackled the ball and the lad (Johnson) went down theatrically. I'm not sure if I can appeal but I'll try."
Brown, who hopes to bring in "two or three" new players before facing Coventry on Wednesday, thinks the incident was a typical example of modern football.
"The game has gone soft," he added. "The yellow cards are being brandished for nothing offences. Referees don't manage the game anymore, they just brandish yellow and red cards."
Dario Gradi thought his Crewe team had lacked the quality to kill the 10-man Rams off with a decisive goal. He said: "The sending-off changed the game to the extent that we were well in control of the game without having the quality to finish them off."
Goals: Rivers (30) 1-0; Bisgaard (49) 1-1.
Crewe Alexandra (4-4-2): Turnbull; Moss, Foster, McCready, Tonkin; Lunt, B Jones, Vaughan, Varney; Rivers (G Roberts, 70), Johnson (S Jones, 79). Substitutes not used: Williams (gk), Walker, Higdon.
Derby County (4-4-2): Camp; Kenna, Davies, M Johnson, S Johnson; Bisgaard (Peschisolido, 85), Thirlwell, Idiakez, Bolder; Smith, Tudgay (Barnes, 73). Substitutes not used: Poole (gk), Holdsworth, Nyatanga.
Referee: I Williamson (Berkshire).
Booked: Crewe Foster; Derby Davies, M Johnson.
Sent off: Derby Davies (61).
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