Despite controlling large parts of their Capital One Cup tie against a brave Carlisle side, the Rams left it late to clinch a 2-0 win.
Jeff Hendrick headed them in front after 62 minutes, but it was not until deep into added time that Chris Martin finished off a right-wing cross to finally put an end to the League Two team's resistance.
McClaren said: "We made hard work of it and should have had it finished a lot earlier, although give credit to Carlisle. We came through in the end and got a second goal, but it was a bit late for me.
"I was pleased with our attitude. It was a full-back game and our two full-backs were excellent, but we should have had more goals. Getting into the last minutes at 1-0 is very dangerous.
"We will get better and the rustiness around goal is something we need to improve on.
"Chris Martin should have scored earlier, but I kept him on to try and get a goal. It's good for strikers to score and it proved worth it keeping him on. Our back players were excellent and kept them quiet, but we need to be more ruthless in front of goal and kill teams off when we get the chances."
Carlisle manager Graham Kavanagh hailed the performance of goalkeeper Mark Gillespie, who has come back after missing most of last season through injury.
He said: "He was magnificent. He's had a nightmare with injury and returned with the bit between his teeth because he doesn't want to lose any more time and opportunities."
Player-coach Paul Thirlwell added: "The lads were magnificent and pushed them all the way. We played with real intensity. To a man we were outstanding and we've show that if we get about teams we can cause problems.
"It was disappointing to concede the first goal, but we went again and just couldn't get an equaliser. They got their second on the break when we were pushing up."
Teenager Kyle Dempsey had an impressive first full appearance for Carlisle and another of Kavanagh's young guns, David Symington, came closest to shocking Derby with a second-half free-kick which was touched on to the crossbar by the fingertips of Lee Grant.
Derby broke the deadlock in the 62nd minute when Jeff Hendrick stole in at the far post to head home a Will Hughes cross.
Rams always looked likely to add to their lead, but had to wait until added time for Martin to kill the tie off.