Tommy Wright’s side will travel to Rugby Park for tomorrow’s Scottish Premiership fixture still hurting from their third qualifying round defeat to FC Minsk.
The Belarusians became the first foreign side to win a European tie in the Fair City after Milos Rnic struck 15 minutes from time to cancel out Steven MacLean’s first-leg winner.
The Serbia international’s strike sent the game into extra time but with no further goals, a penalty shoot-out was required.
But Saints kissed goodbye to hopes of landing a £1.1 million boost and place in the group stages when skipper Dave Mackay, Paddy Cregg and MacLean all missed from the spot.
However, Millar insists the wrong team went through to the play-off round. He said: “We’re a better team than Minsk – there is no doubt in my mind. Over the two legs I thought we had done enough to get through but we never. We missed three penalties and that’s it now.
“Football can be a cruel sport sometimes and it hurts. There are strong characters in that dressing room and the manager is a strong character as well.
“It was great all the plaudits we got during these last few weeks and we enjoyed it, but the bread and butter is the Scottish Premiership and that is what we have got to focus on.
“Thursday night was a time for reflection and mourning. But now we have to try and pick ourselves up. The boys are despondent right now but come Sunday we will be ready for Kilmarnock. There’s no doubt, we’ll be firing on all guns for that game. We want to continue on our good run.”
Kilmarnock boss Allan Johnston believes St Johnstone will be looking to make amends tomorrow.
He said: “I am sure they will be desperate to make up for that, I don’t think it will affect them too much. Obviously the game went to extra time as well so we will need to make sure we play at a high tempo.”
The Ayrshire side are looking to get their first points on the board after losing their league opener 2-1 at Aberdeen last week.
Johnston said: “We didn’t deserve to win the game at Aberdeen so we need to improve as a team.”