Ba's brilliant volley was enough to earn a 1-0 quarter-final replay win over Manchester United on and Chelsea will now face Manchester City at Wembley on 14 April.
The Blues are also through to the quarter-finals of the Europa League but boss Rafael Benitez says his highest priority is to finish in the top four of the Premier League, guaranteeing Champions League football next season.
However, Ba said: "The Champions League is very important but we want to win some trophies as well.
"We know that we are doing very well in two competitions, the FA Cup and Europa League, and we're going to do everything to win them both.
"I've not yet won a trophy. I'm looking for it and I'm looking forward to the semi-final.
"We're going to play against one of the best teams in the country (City), and it's going to be a tough one, but we will go there to win."
Chelsea goalkeeper Petr Cech was the other hero on Monday, producing an incredible save to keep out a Javier Hernandez header and ensure the score remained 1-0.
"I knew he was there and I had to go as fast as I could and take up as much space as I could," said Cech, who rates it his best save of the campaign so far.
"He headed it the other way and I was quick enough to tip it over with the opposite hand."
The keeper added: "It's always important to beat big teams for the confidence.
"We wanted to book a place at Wembley, we seem to have a special relationship with the FA Cup. We treat it with respect and every season we try to win it.
"We have another tough game against City but it's a semi-final, so you expect a tough game.
"We are not having such a fantastic season in terms of the league but it shows we can still beat the top teams and it gives us confidence to play another game on Thursday.
"We have another semi-final to book in the Europa League and hopefully we are going to go through."