The Blues remain on course for a fifth FA Cup win in seven seasons after Ba's second-half strike earned a 1-0 quarter-final replay win over Manchester United and set up a last-four Wembley clash with 2011 winners Manchester City on April 14.
Chelsea interim boss Rafael Benitez afterwards admitted a top-four place in the Barclays Premier League is the over-riding priority this term - the consequences of missing out on Champions League football could be cataclysmic for the 2012 European Cup winners - but Ba wants to win the first trophy of his career too.
The 27-year-old January signing from Newcastle 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."
Ba scored his fifth Chelsea goal in the win, acrobatically volleying in a lofted pass from Juan Mata.
The Senegal striker is ineligible for Chelsea's next game - the third of six in 16 days - against Rubin Kazan in the Europa League quarter-finals on Thursday.
Goalkeeper Petr Cech, who, like Ba, made a crucial intervention against United, is eager to back up the win against the Russians.
"It's always important to beat big teams for the confidence," Cech told chelseafc.com.
"We wanted to book a place at Wembley. We seem to have a special relationship with the FA Cup; we treat it with respect, every season we try to win it and we get something back.
"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."
Benitez was criticised after making seven changes for the loss to Southampton which saw Chelsea's grip on Champions League qualification slip.
Yet after the win the Spaniard described the Blues' season, which has often been on the verge of full-blown crisis, as "a great season, at the moment. It could be even better".
Benitez will have been thankful for Cech's ability as United thought they had an equaliser, only for the Czech goalkeeper to stick out a left hand to save from Javier Hernandez.
"It was a great cross, fast," added Cech, who believes it was his best save of the campaign.
"I knew he was there and I had to go as fast as I could and take up as much space as I could.
"He headed it the other way and I was quick enough to tip it over with the opposite hand."
Meanwhile, Belgian goalkeeper Thibaut Courtois, seen as Cech's long-term successor, could return to Stamford Bridge next term, depending on who is appointed permanent Blues boss.
The 20-year-old is currently on a second season-long loan spell at Atletico Madrid, but says the Blues want more time to consider whether to allow him to stay for a third campaign.
Courtois said in Spanish sports daily AS: "My future is unclear, it's the same as I have said in the past few weeks.
"I was hoping that this week I would find out what will happen, but Chelsea have asked for a bit more time, perhaps because they are going to get a new coach.
"I don't know what will happen but I will have to wait a little longer before I find out."