McClaren told Sky Sports News: "This is management and it can be cruel at times.
"You live and die by results. But Bolton were unlucky at Wolves last week, were terrific at Chelsea in midweek and today we played very well.
"When the pressure is on you need a performance from your players. We have all been in that situation and we all feel for each other. I will have a beer with Dougie and hope performances and results improve because he has good players."
Derby are sixth in the Championship following their win.