The Lanarkshire side were embarrassed by Reykjavik minnows Stjarnan this week and crashed out of Europe yet again at the first hurdle - the fourth time in a row they have failed to get past the opening tie and their 10th consecutive winless game.
Former Dundee and Aberdeen keeper Twardzik admitted he was disappointed he was unable to keep out Atli Johannsson's 25-yard volley winner deep into extra time, despite getting both hands to it.
Twarzik - a product of Bayern Munich's youth academy - faces a battle for the keeper's spot at Fir Park, with Faroes international Gunnar Nielsen pushing him all the way.
And the Czech youngster admits this season is massive for him.
He said: "For me personally it's a very big season. I have a huge opportunity here. I've been given the trust for the two games and I hope it continues.
"For four years I have always been back-up to great goalkeepers and I hope this is the time now that I can play the full season.
"I don't know yet if I am established. I have to show it every single day to get the trust of the gaffer and I hope he keeps putting me in. It's up to the gaffer.
"I can't believe we lost the game. I think I played OK, but I should have definitely done better with the third goal. I'm disappointed to lose a goal from there. It doesn't really matter how much the ball moved or not, I think I should have saved it. I did get a touch on it so that's disappointing for me.
"If I didn't get a hand on the ball, I would have said, fair enough, it was a good strike, but I've got both hands on the ball and couldn't push it out. So I am disappointed.
"I think we should have closed the game down with another goal, but we couldn't manage it. We should have done better at keeping the score at 2-1.
"It's up the gaffer to do what he thinks. I don't really know if that will cost me my place. I definitely hope not. I think I have played OK in my last two games, but mistakes happen."
Motherwell are now on a serious downer ahead of the big kick-off after their defeat in Reykjavik.
They shot themselves in the foot by throwing away leads and giving away three penalties in the course of the tie.
But 23-year-old Twardzik is sure the Lanarkshire side can over-achieve again this season, after last term's superb second place finish.
He said: "There's still a week to go before the start of the Scottish season. I don't think there is any doubt that this team can finish second.
"We still have most of the players that we had last year so the quality is still there."
"I wouldn't say we need new players, but it's up to the gaffer if he needs someone else. We have quite a small squad, but we still have plenty of quality."
And Twardzik agreed with his boss Stuart McCall, who insisted there was no embarrassment in losing to a side of part-timers like Stjarnan.
He pointed out: "Well I wouldn't say they are part-time. They say they are, but they still train five times a week and play at the weekend.
"They definitely had quality up front to be fair. We were the better team though, but we didn't manage to win the tie."