Peter Lawrence said instead of organising a band to play at his daughter’s local pub, The Nag’s Head, in Heworth, York, he would spend her birthday at home “keeping very quiet”.
He said while the fifth anniversary of her disappearance was approaching, her absence felt as raw now as it did after she failed to turn up to the University of York for work on March 19, 2009.
Ms Lawrence spoke to her parents by telephone on the night before and has never been seen or heard from since then.
North Yorkshire Police believe she was murdered and their investigation is ongoing.
At one stage, more than 100 police officers were involved in the investigation and the search for Ms Lawrence extended to the Republic of Ireland and Cyprus.
Mr Lawrence, 67, said: “It sometimes feels like yesterday, sometimes much more than five years when I was with Claudia.
“It is just something that’s there day to day and hour to hour.”
He said he used his work as a solicitor to distract himself and that he did not know if he would have been retired by now had Claudia been around.
Claudia and her family came from Darlington and later moved to Malton, North Yorkshire, where she was brought up.
Mr Lawrence said: “I find it difficult to cope with, but it is not going to go away, so work during those hours stops me thinking about it.
“The support I receive from the community, not just in York, but with people recognising me wherever I go, and acknowledging the situation, does make a difference.”
He said he remained positive about a breakthrough in the case following North Yorkshire Police completing a forensic re-examination of her house and “what appears to be a total reinvestigation”.
Mr Lawrence said after holding a meeting with the force’s chief constable Dave Jones and the launch of the force’s first major crime team, he felt the investigation had fresh impetus.
“The major crime team is a significant move and I think it is experience that counts.
"However, we are very much reliant on somebody having a conscience.”