Dwight Gayle has joined West Brom as part of the deal.
"I said two months ago what we needed, and 10 days before the start of season we have four or five players we thought we could bring but we haven't - and we still are where we are", concluded a frustrated Benitez.
"The clubs were talking for a long time, and now I'm focused on the season to help my team-mates to get the points to do well this season".
With the club's opening Premier League fixture against Tottenham Hotspur less than a week away, the decision on the players' behalf not to speak to the media will come under widespread scrutiny if they uphold their stance.
Venezuela worldwide Rondon becomes Benitez's sixth summer recruit, following on from the signings of Martin Dubravka, Kenedy, Yoshinori Muto, Fabian Schar and Ki Sung-yeung.
Every top flight club must assist the Premier League's host broadcasters as they gather video footage ahead of the new campaign.
"The manager attracted me", Gayle told West Brom's official website. The club's profit stands at around £28 million without taking into account the money from TV rights - and Newcastle are scraping by.
Rondon was a standout performer for the Baggies but could not prevent Darren Moore's side from dropping down to the Championship.