Despite losing their opening first-round group match to Zimbabwe, Ireland battled back to beat Scotland and then trounced the West Indies, the two-time champions, to guarantee their progression.
They stay in Hobart to take on Sri Lanka on Sunday and England are next on Wednesday at the MCG, while Ireland also play against Afghanistan, hosts and defending champions Australia and New Zealand.
"Especially after losing the first game against Zimbabwe, there was a lot of pressure to come back from that kind of situation," Singh said.
"To get through the round is obviously a huge achievement for the team. Now it's just the exciting part, we're looking forward to playing against some of the bigger teams and hopefully cause a few upsets."
Paul Stirling's 65 not out and an unbeaten 45 from Lorcan Tucker secured a momentous nine-wicket victory over the Windies as the Irish moved into the second round of a global competition for the first time since 2009.
"That was one of the best days in Irish cricket and it was great to be a part of it," Singh added. "Everyone was so excited and just still wired after the game.
"I couldn't sleep myself until 3am or 4am just thinking about the game. It was a great occasion overall. You get a lot of confidence from that kind of a win under such a pressure game."