A patched-up Rovers side were second best for long periods at The Den but they held firm to set up a replay at Ewood Park.
Appleton said: "I was delighted with the way the lads went about it. I had three or four players who were only 60-70 per cent fit and we've got another chance to get through.
"It's always going to be a battle when you come to The Den with the Millwall fans behind them.
"It was difficult because the ball was changing hands that many times, I'd be surprised if there were three or four consecutive passes in the whole match.
"The game on Wednesday is going to be a completely different game."
Appleton also confirmed that Danny Murphy had been formally relieved of the club captaincy, with Scott Dann his replacement, but would continue to be available for selection.