Some mistakes I've made in the endgame?

A league match in London. I'm black. I made a blunder 26...Rc3 , but felt I could've done better still. I ended up having less than a minute without increment and blundered the game away..

How can I improve the endgame? Thanks in advance!

I think the best suggestions will be given by the machine. 39. ... Rg2+ (40.Kh3 g5) shouldn’t be bad. =

41. ... Rd2 is easier whereas 42. Rd4?? would even lose for White.