Saturday's early kickoff saw the non-league Imps knock Premier League Burnley out of the competition thanks to a 1-0 win, an achievement praised by the Italian.
The result sent shockwaves through English football as it was the first time for over a century that a team outside of the Football League made it this far in the tournament.
Chelsea joined Lincoln in the quarter-final draw as Pedro and Diego Costa scored second-half goals to claim a 2-0 win over Wolverhampton Wanderers, who had beaten Stoke City and Liverpool to reach the fifth round.
Conte told Sky Sports News: "This challenge was very tough, but we all knew [that]. Above all after the result [at Turf Moor]. I tried to warn the changing room about the difficulty of this game, of this competition.
"It's important to understand nothing is easy. If someone thinks in the league Chelsea for sure become the champions and in the FA Cup for sure you can win this trophy... it'll be very difficult.
"This is a great achievement for [Lincoln] and also this is the beauty of football and the FA Cup. I'm pleased to live this story with them. Now we are with Lincoln in the quarter-final. It's fantastic."
The Blues, Premier League leaders by eight points after drawing at Burnley last weekend, are still on for a possible league and cup double.