Shrewsbury were drawn against the joint favourites for the competition in the last 16.
The tie will take place at New Meadow in the last week of October after they overcame Norwich City of the Championship in the third round of the competition, but has stressed the importance of his side to play to their best in the league games that take place between now and their meeting with the Blues.
Mellon told Sky Sports: "Obviously, we're delighted with the draw and we're all really excited. I think it's reward for how the boys have done in the previous three games that they deserved a big tie, especially at home. I don't think they come much bigger than Chelsea so everybody seems really excited about it.
"We've got six really massive 'bread-and-butter' games in between now and that Chelsea game. What we are going to try and do is use the energy that will obviously be about the place to get a little bit more than possible out of the lads for these massive six games before we even think about Chelsea. We know all about Chelsea and how fantastic the players are that are there, a terrific manager, and when that comes around we'll be very excited about it and go and have a right good go, and see what happens."
The League Two side face trips to Southend United and Plymouth Argyle before hosting Cheltenham. That's followed by a trip to York City before two home games against Bury and Portsmouth before they welcome the Premier League leaders.
Shrewsbury will be looking to build on their solid start to the season which sees them sit in the play-off spots and within five points of the top of the table.
Chelsea, however, will be looking to target the League Cup as the first trophy of Jose Mourinho's second spell in charge of the club after they overcame Bolton Wanderers at Stamford Bridge last night.