Claudio Ranieri and Steve McClaren both admitted their respective league campaigns were the priority as the FA Cup continues to lose its shine.
The two managers made 18 changes between them for Wednesday night's replay, rendering the tie an unwanted distraction.
With Premier League champions Leicester facing a crucial clash away at relegation rivals Swansea on Sunday and Derby targeting a Championship play-off spot, extra time was not what either club wanted.
Goals from Onyinye Ndidi and then Demarai Gray in the additional half-hour did the trick for Ranieri's men to set up a trip to Millwall in the fifth round later this month. Andy King, captain for the night, headed Leicester in front at the start of the second half but Abdoul Camara's deflected free-kick brought Derby level just after the hour.
While the victory might be important for Leicester's confidence after a miserable run of results in the league, Ranieri readily admitted he would swap the cup win for Premier League points while Derby boss McClaren would scrap FA Cup replays altogether.
''I say many times I would change for points but it is not possible,'' said Ranieri, who on the eve of the game was given the vote of confidence by owner and chairman Vichai Srivaddhanaprabha - in attendance on Wednesday night.
''It (Swansea) is the main match of the season, one of the main matches, because we have to do the result.
''But tonight is important to get through and important for confidence. I hope this match can help us improve our Premier League season.''
In his statement backing Ranieri, Srivaddhanaprabha offered his manager his ''unwavering support'' and Ranieri revealed the Thai businessman came to see him and his players before the game.
''It is important because when he comes he is positive every time,'' said Ranieri. ''He brings a positive strength with him, it is important for everybody.
''I speak with the owner but this is normal. He did not come to see me but to see the squad.''
Football Association chairman Greg Clarke was in the stands at the King Power Stadium and must not have failed to notice that clubs now see the FA Cup as a distraction.
McClaren, who made eight changes ahead of a home game against Bristol City on Saturday, called for the FA to look at getting rid of replays, in another blow for the oldest cup competition.
''Our main focus is the Championship and the play-offs,'' said McClaren, who won the FA Cup as assistant manager at Manchester United in 1999.
''Both teams tonight didn't need extra-time and I think the FA need to look at the competition and maybe have one tie.
''We played at Pride Park two weeks ago and it was a great occasion, a great atmosphere. It was 2-2, imagine that game going to extra time and maybe penalties.
''Two weeks on and it was two different teams. There was no way we couldn't not make changes with the schedule we have coming up.
''A lot of Premier League and Championship managers made changes in the first game, we didn't. We took it serious, as did Leicester. But with the schedule, players can't play at the level required - Premier League for Leicester and Championship for us.
''I think it is something the FA should look at.''
Asked if he thought FA Cup replay should be scrapped, Ranieri was not as forthcoming.
He said: ''I don't know, I don't change the rules. If they want to make changes then for me it is okay. The rule is the rule, I am happy.''