"I do the footballing side; other people do the financial side," Strachan told BBC Tees. "We talked [about O'Neil] and this is the best decision."
The midfielder signed a new contract in December to stay at the club till 2012.
Middlesbrough have not explained what future O'Neil now has on Teesside.
Reports from Portsmouth have suggested the financially stricken south coast club believe Boro are seeking to renegotiate the payment.
But Middlesbrough chief executive Keith Lamb said: "I'm surprised by the comments attributed to a Portsmouth spokesman.
"All of our payments to Portsmouth related to Gary's transfer are up to date and I can assure the club and their administrator that should any further payments become due under the terms of the transfer then we will, of course, honour them."
First-team captain O'Neil joined Middlesbrough from Portsmouth in August 2007 for a fee of £5m, and has made 34 appearances this season.