Drogba lost his rag when Lampard took their first-half penalty after manager Carlo Ancelotti had made the England midfielder the designated penalty taker.
Asked about Drogba's childish reaction to being denied the chance to take the first penalty to make it 2-0, Lampard said: "It was nothing. That's what makes Didier what he is. He's hungry.
"It's 1-0, I've been taking the penalties all season and I wanted to score to make it 2-0. Once we went clear then I was more than happy for Didier to go and try to win the Golden Boot.
"We're a team and we want him to do well. He did it and he deserved to be top scorer."
Drogba himself was apologetic afterwards.
"I understood," he told Sky Sports 1 about the first penalty. "But at the same time I was disappointed because at 1-0 I wanted to score. I had to get over this frustration and in the second half come back.
"We did so well today I knew I would have some chances to score. I was not happy at first but after, I knew I was making a big mistake and Frank was right."