Sri Lanka beat Zimbabwe by 74 runs on Saturday to claim the final place in the last four where they will play favourites Australia on Tuesday.
"India was a disappointment but the guys knew this was an important game," Jayasuriya said. "If we win we were in the semi-finals and if we lost we were out.
"What happened in Johannesburg was a disappointing all-round performance altogether. But we have played enough cricket to come back and play well."
Although the pitch was clearly difficult for batting during the Sri Lanka innings, Jayasuriya said he felt it had improved once the Zimbabweans started their run chase.
"The pitch was very slow in the morning but when we were bowling it was a good wicket," he said. "They started really well against our fast bowlers.
"Our spinners found it a little difficult to turn the ball but later on Murali (Muttiah Muralitharan) came on and bowled a good line and Chaminda Vaas bowled some good reverse swing. That is where we changed the match.
"Earlier on Marvan (Atapattu) batted well because the wicket was not easy at all."
Atapattu was named man-of-the-match after batting through the Sri Lanka innings for 103 not out.
Looking forward to Tuesday's match, Jayasuriya said although his side were heavily beaten by Australia in the Super Sixes, conditions at St George's Park could favour his side.
"The first match is over now and history. The semi-final will be a different game altogether," he said. "History says that Port Elizabeth has been a turning track. We have to go there and see but it usually turns and that would suit our bowlers."
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