Good lord, love, it's just a bike ride !
Sure it would have been nice if you were able to keep up with the new group right off the bat, and it sux when you realize you're not yet as good as you'd like to be, or think you should be, but these things take time.
Stop beating yourself up and go back and ride some more with that faster group. You'll get better by pushing yourself. It sounds like the group leader was encouraging you, whether or not you wanted to hear it at that moment. Soon, maybe not tomorrow or the day after, but soon, you'll be able to keep up with them.
Then when a new person comes along and is in the same boat as you are now, you can 'pay it forward' and encourage him or her.
2009 Lynskey R230 Houseblend - Brooks Team Pro
2007 Rivendell Bleriot - Rivet Pearl