Posting on Instagram, the Belgium captain wrote: "Never meant for my words in the press yesterday to offend anyone or undermine the institution of Aston Villa Football Club which I massively respect and I'm grateful to for the past three years.
"I must however admit my mistake and apologise for my choice of words, (I) will be more careful in the future. Wishing the club the best in the future. Youri."
The apology followed remarks Tielemans made to reporters during United's pre-season tour of the Republic of Ireland, in his first extended sit-down with journalists as preparations for the new campaign entered their final stretch. Asked to reflect on his summer switch, the 29-year-old had struck a grateful tone before comparing the size of the two clubs.
"I am very thankful to Aston Villa. I owe them the world," he said. "It is a great club, we did amazing things, and they have put me back to my best level. But there are clubs above Villa, and Manchester United is one of them. It is a great achievement for any footballer to end up here.
"It means you have done well in your career. But it does not end there. I want to be successful."
Manchester United triggered the £35m release clause in Tielemans' contract this summer to bring him to Old Trafford, where he has joined Michael Carrick's midfield as part of a rebuild in a position that has troubled the club in recent years.
He ended a three-year spell at Villa Park during which he helped end the club's three-decade wait for a major trophy, scoring in Aston Villa's Europa League final win earlier this year and making 134 appearances in all competitions for the Midlands club after joining from Leicester City on a free transfer in 2023, where he had previously helped the Foxes win the FA Cup in 2021.
Tielemans has already spoken positively about settling into his new midfield alongside Bruno Fernandes, describing the partnership as coming naturally.
"It's really natural," he said of the Portuguese international. "He is a guy that can find space easily."
Carrick's side open their Premier League campaign away at newly promoted Hull City on August 22, with Tielemans expected to be a regular fixture as United look to build on the improvement that saw Carrick guide them to a third-place finish and Champions League qualification in his 16 games in interim charge after replacing Ruben Amorim in January, form that earned him the permanent job in May.