United were docked three points and fined £30,000 by the league. Part of the fine is suspended.
The club labelled the punishment “wholly disproportionate for what was a simple honest, human error”.
Ali Coote, who came on as a 76th minute substitute, and Jamie Robson, who was an unused sub, had not been registered by United.
United won the match 3-2 – only their seventh league win of the season – but will now lose the points.
A statement from the club said: “Chairman Stephen Thompson has resigned from his position on the SPFL board with immediate effect.
“He has expressed his shock and anger at the severity of the sanction imposed by the SPFL in relation to a rule breach in our recent Ladbrokes Premiership fixture versus Inverness Caley Thistle.
“Whilst acknowledging the club’s error and accepting a breach of rules occurred, the chairman feels the gravity of the punishment is wholly disproportionate for what was a simple honest, human error.
“We await the full written judgment after which we will consider our next action.”
United claimed their supporters had been punished for the error.
“Our travelling fans are the ones who have been punished the most here and the club will examine ways to make this up to them,” the statement added.
United officials attended an SPFL disciplinary hearing omn Wednesday where they pleaded guilty to breaches of player registration regulations.
The match will not be replayed.
A statement from the league said: “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 £30,000 (part suspended).
“The disciplinary hearing concluded that replaying the game before the end of the season was not practical.”
Coote replaced striker Simon Murray when the score was 3-2 to United.
The midfielder had previously spent time on loan with East Fife, helping the Methil club to lift the League Two crown.
It meant he didn’t return to Tannadice until the very end of April, with SPFL rules forbidding such loan players from playing again for their parent club if they returned after 31 March.
Robson had only recently returned from a loan spell at Brechin.