United were denied a famous win by a deflected injury-time strike from 25 yards at Tannadice on Thursday night after Keith Watson put them ahead for the second time in the first leg of the Europa League third qualifying round.
Although United goalkeeper Radoslaw Cierzniak made several excellent saves, United also created a number of chances after Willo Flood's 37th-minute opener.
Mackay-Steven, whose team host Hibernian in the Scottish Premier League on Sunday, said: "All the boys are absolutely gutted with that killer punch at the end.
"I thought we played well and it's a sickener that the boy cut in and it took a deflection and it landed in the top corner.
"We'll dust ourselves down and we're quietly confident going over there that we can get a result.
"The team is really confident and all the boys that have come in have done well. All the boys on the bench are keeping the ones that are starting on their roes."
Houston compared Mackay-Steven favourably with Dinamo's ?15million winger Balazs Dzsudzsak after a second-half performance that left Australia right-back Luke Wilkshire struggling.
However, the Scotland Under-21 international shrugged off compliments about his own performance.
"It was pleasing but I felt the whole team did really well," he said.
"We were solid at the back and we created chances. The crowd were great, they really helped us.
"It was a sickener at the end but we'll go over there and give it a go.
"We're always at our most dangerous when we attack teams.
"I fully believe we'll go over there and attack and create chances because that suits our style of play."
Houston has challenged Mackay-Steven to make a flying start to the season after the winger took time to fins his feet in his debut season before earning young player of the year nominations.
"The first few games of the season set you up and get you in your stride," Mackay-Steven said.
"I'll be looking to start the game positively on Sunday.
"All the boys are just hitting the ground running now. We are jumping at the bit and can't wait for Sunday."
