Former Chelsea and England midfielder Lampard insisted that it is too early for alarm bells, but acknowledged that his side must learn from the defeat going forward.
"It was tough, we were well beaten by the better team on the day. We went into the game under no illusions and knew it would be difficult for us. There were no surprises but we didn't deal with them. They are a good team, had more energy with the ball and without it so lots of lessons for us really," he told reporters.
"We can't get too down because we are two games in and there's a long, long way to go but lots of lessons we must improve on. The most disappointing thing for me is we went away from what we are.
"Leeds have come to our place and looked more confident than us. it comes down to the basics of football, if you don't move the ball quickly enough and you're not brave enough and your quality is not quite good enough then it's hard to get out and we weren't good enough today.
"That's not to say we're not good enough, we certainly are but we need to be braver and can't play longer balls when we should be trying to get out because that's an easy option. I'd rather people take a chance and try and play out in a positive manner than not so great lessons for us today."
Derby are back in action again on Tuesday when they face League Two side Oldham Athletic in the EFL Cup.