From the first vid I saw, I thought you were 10 times better! But, that said, even when you think the act before you is better than you, you have to remember that you're not the audience.
I've been up after comics that got much bigger laughs than I ended up getting--but you know what, I still think I'm funnier! LOL
Of course, you can always begin by giving the great band before you props...asking for another round of applause for them. You're all part of the same show, and although the business is competitive, you don't need to make a show that...it's a cooperative effort to make a good show for the audience.
If you ever want a warm up act that sucks so you sound better...give me a call! I know all the words to Ave Marie and La Donna Immobile...and also UB40's 'Reggae Music.' I'm sure I have a horrible singing voice, so would be glad to help you out!