Giggs swept past the landmark in the Luzhniki Stadium last May, notching up his 759th appearance as United overcame Chelsea in the Champions League Final.
"People kept asking me about the appearance record when I was trying to win the Premier League and Champions League, so it is a relief not to have it there any more," the 34 year old told Inside United.
"Of course I am proud to have done it but now I just want to move on, hopefully add a few more games to the total and focus on the team."
Giggs has achieved so much in the game but worries about the pressures modern players are under.
"There is a stigma of celebrity and money alongside football these days, which is different from when I first came into the team," he said.
"Now you see players with nice cars and 18-year-olds on good money.
"But it's down to the individual having the right attitude and application - it's not enough just to have the talent.
"I have seen players with plenty of ability, no shortage of that whatsoever, but they didn't make it because they did not have enough hunger to sacrifice things in order to succeed."