The Hoops' 1-1 home draw against Inter Milan on Saturday - where a wonderful Kris Commons strike just before the break was cancelled out by Rodrigo Palacio in the final minute - saw them put in a much better performance than their 4-0 thumping by Ajax last weekend, which was followed up by their 1-0 defeat to Norwich at Celtic Park in midweek.
However, it left Neil Lennon's men with one win in six warm-up games ahead of the visit of the Finnish club for the first leg of the third qualifying round match.
The Wales full-back, though, saw enough against the Italian giants to give him confidence.
"We haven't done ourselves justice this pre-season performance-wise. Ajax was an eye-opener for us. I think that is where we want to be and we showed we have improved since," said Matthews. "But yesterday I think it all came together. I think everyone played their best game of the pre-season so it is a good sign for us.
"We started the game well and kept it going and were unlucky not to get a victory in the end. We pushed a top class team all the way and I thought we deserved to get the win."