Hearts manager Jim Jefferies reflected on a job well done after their 1-1 away draw against Paksi but warned his players against complacency.
Jefferies' men hold the advantage of an away goal for next week's return leg.
Paksi recovered from a 1-1 home draw to beat Tromso 4-1 on aggregate in the last Europa League qualifying round.
"I'm sure at Tynecastle it'll be a different atmosphere and a different scenario and hopefully we can finish the job there," said Jefferies.
"You've got to be careful with complacency. To be fair to them, they're a stuffy side.
"They get behind the ball and they make it hard for you and they compete well. You can see why they've been doing well recently and why they had a good result in Tromso.
"I think they'll face a tougher test [at Tynecastle]. We showed that we were very comfortable.
"I'm sure the boys can take belief that they can go and it's all in their hands now. The job's been done here."
Hearts fell behind when Istvan Sipeki opportunistically lobbed goalkeeper Marian Kello.
But Jamie Hamill's penalty, awarded after John Sutton had been hauled to the ground at a free-kick, drew the visitors level before the break.
"I thought we were in control of the game," said Jefferies. "Their goal was a bit of luck. Ninety-nine times out of 100 he wouldn't do that again. It was a bit of a shock.
"Their boy was warned before once by the referee and then John Sutton said it was a rugby tackle that pulled him down.
"We had the best chances in the second half.
"Overall, the objective was to make sure the tie was alive and not to lose the game even though we set out to win it. The away goal's precious."
Ryan Stevenson replaced Sutton and was then himself substituted after picking up an injury.
"He got a really bad gash on the back of his hand which required six or seven stitches," explained Jefferies.
"It just went right through to the bone really and it was a nasty one but I'm sure he be not too bad.
"He'll maybe not play golf for a wee while but he should be OK."