Rodriguez left the Toffees on Wednesday to sign for Qatari outfit Al-Rayyan for an undisclosed fee.
After joining from Real Madrid 12 months ago, the 30-year-old went on to make 26 appearances in all competitions for Everton, scoring six goals, in an injury-disrupted 2020-21.
Speaking about Rodriguez at his pre-match press conference on Friday ahead of Saturday's home clash with Norwich, Benitez said: "James is a very easy and complicated issue.
"That is the Premier League, that is Everton Football Club, that is intensity from day one until the last day, and then when you have a player in the situation that we have, that can be available just 50 per cent of the games, overall, in the Premier League, it is not something that we can manage easily.
"We have to maximise the resources that we have, and that is the situation."
Benitez - who succeeded Carlo Ancelotti who brought Rodriguez to Everton - added with regard to the playmaker: "It is not easy to find good offers when you want. You have to manage the offers when they are there, and that was the time.
"We couldn't find the right ones before, that was the right one for him, he's happy with that and we have to do it because we have to maximise our resources and then we have to be sure the long-term future of the club is protected."
Benitez was asked if Rodriguez leaving meant more funds for Everton in the January window, and he said: "Yes, I think so. I had that conversation yesterday with Mr Moshiri (Everton owner Farhad Moshiri) and we are lucky enough to have owners that want to spend money.
"It is just to be sure that we can do it in the right way, but I think they are very keen to spend the money and improve the team.
"Then we need to find the kind of players we need to find, players that will be OK, adapted to the Premier League, but at the same time try to bring some quality that will improve the level of the team.
"That is the difficult thing to find, this balance between we want to spend money on very good players, but at the same time they have to be good players for us, in England, in the Premier League, and for Everton Football Club."
Benitez also revealed Everton had Jordan Pickford back available, along with Lucas Digne. Goalkeeper Pickford has been out of action after suffering a shoulder injury against Burnley on September 13, while full-back Digne sustained a calf issue in Tuesday's Carabao Cup tie at QPR.
Benitez said: "Pickford is OK, he has been training. Lucas has been training. The others are exactly the same situation - they are getting better but still not available."
The list of players Everton still have sidelined includes forwards Dominic Calvert-Lewin (quadriceps), Richarlison (knee) and captain Seamus Coleman (hamstring).
When Benitez was asked about the trio's chances of playing for their respective countries during next month's international break, he said: "No chance. They will not be available, (I'm) almost 100 per cent sure."
Everton have announced an investment package of up to £45million to support the delivery of their new stadium at Bramley-Moore Dock and the Goodison Legacy Project has been approved by the Liverpool Combined Authority.
Council leaders voted in favour of a grant of up to £15m to assist with infrastructure work, as well as giving the green light to a loan of up to £30m towards the overall project.