The Premier League outfit trailed their League One counterparts 1-0 at the interval courtesy of Chris Porter's strike on the half-hour mark.
Although the Cottagers leveled matters with 15 minutes remaining through Hugo Rodallega, Meulensteen's men failed in their quest to find the winner, resulting in a replay at Craven Cottage.
"I'm not happy with a replay, I don't think that is the right word because looking at the second half and the red card you should - as a Premier League team - be able to put the game to bed," the Dutchman told Sky Sports News.
"We lacked a bit of quality. In hindsight we were a bit lucky to still be in the cup because one of the breaks they had could have hurt us and they had a penalty shout that could have been given."
Both outfits will discover who they can expect to meet in the fifth round of the competition later this evening.