The defeat to Paolo Di Canio's relegation-threatened side effectively ended the Toffees' challenge for a Champions League spot, leaving them six points behind fourth-placed Chelsea having played a game more.
|66/1||Everton are 66/1 with Paddy Power to finish in the top four
"Everybody was perhaps a little bit tired [on Saturday]," Fellaini told the Liverpool Echo. "It was disappointing for the team and the staff. There weren’t a lot of chances.
"Sunderland were playing at home, for a new manager in his first game here. They had a lot of energy.
"It was a very difficult game for us. It was a bad goal to concede with the mistake, but football is like this. When you concede a mistake, it’s difficult to win the game."
Fellaini is refusing to give up on a fourth-place finish after morale-boosting draws with positional rivals Tottenham and Arsenal, and has eyed victories over Liverpool and Chelsea before the end of the season.
"We have four more games and we must keep going and try to win," he added. "It's difficult now but if we try, we will see at the end of the season.
"We have four more big games - two at home and two away. We will try to win those two at home and we will see where we are after Liverpool and Chelsea."