Boro secured their second successive high-profile Premier League scalp in exhilerating fashion on Tuesday night when they saw off Antonio Conte's Tottenham Hotspur in front of a sell-out home crowd and nationwide audience of millions.
It followed their dramatic penalty success in the previous round against Manchester United at Old Trafford.
Boro have now been handed a third successive draw against a top-flight big gun in the shape of Chelsea, who will visit the Riverside Stadium later this month for another eagerly-anticipated tie.
Before that, play-off chasing Boro have some key Championship games, starting with Saturday's 'six-pointer' with Luton. After that, they visit Wilder's former club Sheffield United in another fixture of top-six significance on Tuesday night.
On the draw with Tomas Tuchel's Chelsea, who edged past Luton 3-2 in round five in midweek, Wilder said: "It is the home draw we were all after.
"When you go deep into the competition, it is what it is. We will all have our little ideas in who we would have liked to have played.
"But the majority of the Boro punters would have wanted a home draw and to have 30,000 of our supporters watching that game and I am sure there will be a huge clamour for tickets against the world champions and Champions League holders at home in the middle of March.
"It is great to be involved in this competition and there is no downside of being involved at this stage, regardless of what games we have coming up and how it might mess about with the fixture list. That is complete nonsense if people think we are worrying about that.
"We want to win games of football and play in big games and have big experiences and we are certainly having that at the moment."
Riley McGree and Aaron Connolly return to Boro's squad for the home encounter with the Hatters.