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Hasselbaink had given Chelsea the lead in the 21st minute with a spectacular left-foot curler from the edge of the penalty area.
"After the first goal we made a lot of chances to close the game but today Chelsea were not very lucky," said Ranieri.
"We had chances with Hasselbaink, Zola, Gudjohnsen and Lampard but that's football. They only shot at the goal twice and the second time they scored."
Hasselbaink was substituted in the 75th minute and Ranieri confirmed he had a slight leg injury which he had been carrying for a week.
"We have been playing a lot of games these past two months, once every three days is very hard," said Ranieri.
"Eidur Gudjohnsen also had a little problem today and he hasn't trained a lot.
"Ideally I wanted him to recover but I decided to put him on for Mikael Forssell to try to close the game."