Potter is expected to utilise his squad again for Tuesday night’s last-16 clash, with Alexis Mac Allister, Enock Mwepu, Yves Bissouma and defender Adam Webster also likely to be in the frame.
Republic of Ireland forward Connolly, 21, scored both goals in the 2-0 win over Swansea in the third round but has since featured only as a late substitute in the 1-1 draw at Crystal Palace.
Potter accepts team selection is never an easy topic to address with players when they are not involved, but expects all of his squad to be ready whenever needed.
“Anytime the guys get to play is an opportunity, that is the life for professional footballers,” said Potter.
“Of course everybody has opinions and it is easy to speak and talk, but actually the best way to do it is to let football speak and what you do on the pitch.
“We were really pleased with Aaron in the last (cup) game. It was nice for him to get some goals.
“We have been picking up points in the Premier League so it is not so easy (on the bench), but that is how life is.
“You have to wait your chance, be patient, you have to keep working, to keep focus on yourself and make sure that if the opportunity comes that you are ready and you can take it.”
Brighton were beaten 4-1 at home by Manchester City in the Premier League on Saturday but nevertheless have enjoyed a fine start to the new campaign – which in itself gives Potter another selection dilemma.
“It is a bit more of a difficult conversation if you are down the bottom of the league and you haven’t got any points, but we have been fourth in the Premier League, so clearly the 11 who are playing are doing okay,” the Albion boss said.
“So sometimes it is the life of a professional footballer, sometimes is not fair, sometimes the coach makes a different decision, and there is competition because it is the highest level.
“All you can do as a player is not let the coach’s decision affect your response really.
“Make sure you are ready, make sure that when you are on the pitch you are doing your best and that you make it difficult for the coach not to play you.
“All you can do is be honest, articulate your thoughts to the player, and then the response is their responsibility.”
Potter confirmed there were no fresh concerns following the City game, with Webster set to be involved again after recovering from a hamstring injury.
Leicester chalked up a third straight win in all competitions with a 2-1 victory at Brentford on Sunday.
Foxes boss Brendan Rodgers will also freshen up his side for the cup tie at the King Power Stadium.
Potter, though, is expecting nothing but a stern test of his own squad’s depth with a place in the quarter-finals at stake.
“Leicester away is a very, very tough game,” the Brighton boss said.
“Brendan will be wanting to be competitive and want to win the game as well with his squad, so we are under no illusions.
“But it is also a great opportunity for our players and we are looking forward to it.”
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