Jones said as much during an appearance on Fox Sports before Errol Spence Jr. beat Mikey Garcia for the IBF world welterweight title Saturday night at AT&T Stadium in Arlington, Texas.
The Giants traded Beckham and defensive end Olivier Vernon to the Browns Wednesday, in exchange for right guard Kevin Zeitler, safety Jabrill Peppers, a first round pick in the 2019 NFL Draft and a third round pick in the 2019 NFL Draft.
Beckham spent five seasons with the Giants, making the Pro Bowl in each of his first three NFL seasons. The superstar pass-catcher faced the Cowboys just once in his last two seasons in the NFC East, but was immortalized for his spectacular one-handed touchdown grab during the 2014 season against Dallas.
"Thank you, thank you, thank you," Jones said on the Fox broadcast.
"When you are in a league, you really want the competition to be there," Jones added.
Jones also praised Browns ownership for the off-season moves, before referencing the Cowboys' need to work on contracts for core players.
"We know we have to put the money in the guys that will get us here," Jones said. "It just happens, we are lucky enough to have Dak Prescott, Amari Cooper, guys that we really need to spend our money on ... DeMarcus Lawrence."
Dallas won the NFC East for the third time in five years in 2018, posting a 10-6 record. The Cowboys have lost in the divisional round of the playoffs in each of those division-winning seasons.