Hi, just to add some value to this once great, but deteriorating forum.
There are many finance professionals with worse credentials than you. With a 2nd upper in EE from
nus, I can safely tell you that you are doing fine. I suggest you setup a Linkedin account first if you haven't, to see how luck & opportunity plays a big role for many average people who got into lucrative roles.
Secondly, if you're keen to join banking/finance, the roles which are more promising and "closer to the money", so to speak, are Treasury front office (sales/dealing), Product Managers, Private Banking (investment consultants/product specialists), and Research (any form of research, eg. Equity, Global Macro economics, Commodities etc) These are the ones you want to go into, to make good ROI of your Masters investment.
3 more real-life tips:
1. Many people who are in those roles i mentioned, were not from top tier universities. Eg. if you do a
SMU MBA/Masters, you could possibly get into private banking without prior finance exp.
2. If you can't get into top tier firms, get into those roles in small firms first. Start from small and gain experience and you will eventually end up in the prestigious ones. DO NOT take the backoffice offer in a big firm over the roles i mentioned in small firms. If you do equity research for 5 years in a small firm, you will more likely end up as a fund manager/trader/M&A analyst than the guy who did 5 years of backoffice work in an IB.
3. You can start with internships if you can't get perm/contract offers for those roles.
I am sure there are lucrative jobs in engineering/IT sales as well, which im not familiar with, so i won't comment on that sector.
Good luck!