The Magpies have began the season poorly, losing their first two games in the Premier League.
However, Ritchie does not want anyone at the club to use the departure of Benitez as an excuse for their poor form.
When questioned by reporters about Benitez, Ritchie said: "You guys, the fans and everyone will all have their own opinions.
"Mine is that we have [to] stick together, continue to work hard, try to improve.
"The group is very similar to what we had last season.
"I still believe the new additions can strengthen us.
"It may take a little bit of time but it is a long season and yes, we'd like to have got off the mark, but we didn't.
"That's certainly not the result we wanted but we have to keep working and obviously improve."