Cambridge dominated the first half and looked well on their way when Tom Youngs fired them in front four minutes after the break.
The Abbey Stadium fans felt confident enough to chant "Claridge what’s the score?" only to get an answer they did not want.
Claridge admitted after the match: "We got something we did not deserve. Cambridge were the better side and we had five or six people not really doing it.
We are lucky to have another go."
Despite being without five first choice players, three of whom were suspended, Cambridge took the game to Millwall form the start and were unlucky not to score when Youngs slammed a 38th minute shot against the crossbar.
Millwall keeper Tony Warner produced a wonder save to push Adam Tann's header for a corner, but it was from that flag kick that Youngs scored his close-range goal.
Millwall looked beaten until a pass from Paul Ifill ran to Claridge who side-footed home on the hour.
Both sides had half chances to win it but the game fizzled out.
Cambridge manager John Taylor said: "I was delighted with our display, especially in view with the players we had out.
“Millwall had one real chance and it had to fall to my old mate Steve Claridge. But we will go there with a lot of confidence after this display."