The champions were beaten twice at Old Trafford last week when Everton and Newcastle United left with respective 1-0 wins.
Keane said that the players need to take more responsibility for the results, but said that a measure of calm is now needed.
Speaking to ITV Sport, the United legend said: "The players have to take responsibility, it is the same group of players as last season [when they won the league]. But look, footballers are human beings and they're just getting used to the new environment.
"It's taking time to adapt but what's needed is cool heads and everyone needs to relax a little bit. One of the biggest problems has been their lack of recruitment in the summer, they've obviously brought Marouane Fellaini in, but they never got their targets.