Lampard has become a regular target of abuse for England fans at Wembley and jeers rang round a capacity crowd on Saturday when Lampard was introduced for Michael Owen during the second-half of the 3-0 win over Estonia.
Although the 29-year-old has shown no sign of being affected by the adverse reaction towards him, McClaren is at a loss to understand why it is happening.
"Two years ago he was voted the fans' player of the year two years in a row and when you look at the three games against Brazil, Estonia away and Germany, he was our best player."
McClaren has been the subject of fan derision plenty of times during his short time in charge, notably in Barcelona last March when England struggled to wear down the part-timers of Andorra.
Having presided over a run of five successive qualifying wins that has taken England to the brink of a place in next summer's European Championship finals, McClaren is understandably keen not to antagonise the supporters he now appears to be winning round.
Instead, he is calling on Lampard to come through his problems and continue to prove his worth to England on the pitch.
"No-one likes being criticised and booed," said McClaren.
"I wouldn't want it at a club and I don't want it at international level either.
"We have talked about it but I don't think it has affected him.
"He just has to get on with it. All I am concerned about are his performances on the field. It is not about who is criticising him or booing him."