I played on .09's for years and still do on my Strat. .11's are a pretty heavy gauge and particularly when you were using a lower gauge before. I use .10's on my Gibson and depending which guitar I've been playing most often, the change is very noticeable for me even when I expect it.

Additionally, new strings do tend to be a little inflexible too. I had a tech show me a trick for 'stage' swap outs (when a tech had to do a string change mid-show; he said to grab the string in the same way you grab the handle of a suitcase and slightly tug on the strings and do this up and down the length of the string as best you ca and do this for a few minutes. It makes the string more elastic and also you don't have to go through the frequent re-tuning phase with new strings. Essentially, you're stretching out the strings since they've never had tension on them and will loosen with time. Make sure that you give it a light tug and don't pull up too hard and break the string.