Grant is convinced his side can turn things around and secure a place in the semi-finals against either Arsenal or Liverpool, whose tie hangs in the balance after they drew 1-1 at the Emirates Stadium.
"We played well in Turkey, not just in the first half but in the second half until they scored.
"Fenerbahce are a good team with a good coach. He was a player I liked very much.
"I know it will not be easy but I know we can win. We have a lot of quality and can beat anyone.
"During December and January nearly all the big players were out.
"This group of players has brought us to the place we are now. They have done a terrific job - so we trust them."
Grant was pleased with the players' response after the defeat in midweek.
He said: "I am always happy when we win. We started well, but Manchester City came back at us. They have a good team and a good manager.
"City put on a good show in the first half, but we played better in the second period and could have scored more."