Ali Coote and Jamie Robson had both just returned from loan spells and should not have been listed by the Tayside club, who were already relegated from the Ladbrokes Premiership
United have also been fined Â£30,000, an unspecified part of which is suspended, following a Scottish Professional Football League disciplinary hearing
Coote had just returned from a loan spell at East Fife while Robson had played for Brechin the previous weekend, and teams are unable to register players from April 1 onwards.
An SPFL statement read: " At a disciplinary hearing today (Wednesday, 11 May, 2016) the SPFL Board charged Dundee United FC for playing (as defined in the SPFL Rules) Jamie Robson and Alistair Coote in their Ladbrokes Premiership match against Inverness Caledonian Thistle on Friday, 6 May, 2016.
"Jamie Robson was an unused substitute in this game
Alistair Coote was listed as a substitute and entered the field of play after 76 minutes when he replaced Simon Murray, at which point the score was 3-2 to Dundee United
Dundee United won the game 3-2.
"Dundee United pled guilty to breaches of SPFL Player Regulations 12, 14(i) and 14(ii), which breached SPFL Rules
The breaches of Player Regulations occurred because the club failed to apply to the SPFL to league register the players as required by SPFL Player Regulations 7 and 3A.
"As a result, Dundee United were severely censured, deducted three points from their points total this season and fined Â£30,000 (part suspended).
"The disciplinary hearing concluded that replaying the game before the end of the season was not practical."
Source : PA