The 18-year-old made his first start since October 30 against the cup holders, who looked like they could be on the wrong end of an upset when Saints striker Jay Rodriguez broke the deadlock.
However, Chelsea rallied before half-time though and went on to win comfortably, with goals from Victor Moses, Branislav Ivanovic and Frank Lampard complementing a double from debutant Demba Ba.
Southampton face the Blues once again in a league encounter at Stamford Bridge in 10 days and Ward-Prowse believes they will be better next time thanks to their experience on Saturday.
"I think they proved why they won the competition last year, why they are where they are in the league and obviously why they are European champions," the midfielder said.
"We contained them in the first half quite well and Jay scored a great goal from a great pass from Jason Puncheon.
"It looked good, but obviously the two goals before half-time killed us really.
"I embrace the challenge of playing such great players. Looking at the players you're playing against, they are international players and World Cup winners.
"It is a great challenge but something I embrace. I learned a lot.
"Individually and collectively we have learned a lot today and it will for sure make me a better player.
"I think our main priority is the league so obviously we'll draw a line under it.
"We will get going again on Monday and plan ahead for the rest of the season so we can stay in the league."