The Premier League outfit were frustrated in the first half as Derby defended resolutely at Pride Park, but the Portuguese's words at the break brought added vigour and urgency to his side.
Goals from John Obi Mikel and Oscar duly secured Chelsea's progress to round four, and Mourinho was pleased with the way his side raised their performance after the interval.
"The game was difficult," he said. "In the first half we didn't play bad, we played quite well but it was still 0-0 and 0-0 at half-time is a big risk because in the second half the opponent score and you are in trouble.
"I think the players got the message we needed extra intensity, we needed to put them in more difficult situations.
"I decided to change (Michael) Essien for Eden (Hazard) and bring an extra attacking player, fresh with speed one against one.
"I knew that could make it more difficult for them. The team played seriously, we won, job done against a good Championship team."
Chelsea's reward for victory over Steve McClaren's side is a fourth-round tie against Stoke City at the Britannia Stadium.
