Michael Ballack and Frank Lampard scored at the start and end of the second leg against Fenerbahce at Stamford Bridge, meaning they will meet Liverpool for the third time in four season at this stage of the competition.
Grant said: "Of course I believe. I am optimistic by nature. I believed that when I received the team after the draw against Rosenborg here and there were five teams ahead of us in the league and I don't know how many points.
"I said that we could do good things this year. Now we are close. So of course."
"This is the first news they told me, that is was Liverpool in the semi-finals," Grant said. "The one thing I always wanted to know is the future. I don't know the future but we will do our best to be in the final."
He added: "I feel good because our target was to be in the semi-final of the Champions League and we did it.
"It was not so easy. In Fenerbahce we played better than we did tonight. It was a nervous game and we defended well because they didn't create chances.
"But the most important thing was the result and that was good for us."
Grant said: "It's a bit disappointing but it has happened. It's not good that he will miss the next game but it is a fact and we cannot do anything about it."