Craig Levein acknowledged the improvement Hearts require ahead of a big week after the 1-1 draw against St Mirren in the Ladbrokes Premiership.
The league's bottom side had the better of a goalless first-half at Tynecastle on Saturday but it was the home side who took the lead in the 55th minute when defender Clevid Dikamona headed in a Olly Lee corner for his first goal in maroon.
However, the Paisley side refused to buckle and came battling back albeit it took an own goal by Sean Clare to give them a second successive draw and offer encouragement for their relegation battle.
Hearts host leaders Celtic in the league on Wednesday night before travelling to Championship side Partick Thistle in the William Hill Scottish Cup quarter-final on Monday week.
"We need to be better on Wednesday," said Levein.
"There are two big games for us. In some ways, the Celtic game will bring a different atmosphere and a different pressure which might help.
"And we need to do as well as we can in that game and pick up points and then we've got the game on Monday.
"We are usually good at getting off to a good start at Tynecastle and that usually gets the supporters right behind us but there was a lack of urgency, speed of passing resulting in what you've seen. So we need to do better."
Buddies boss Oran Kearney praised the contribution of Czech keeper Vaclav Hladky who was solid on the occasions when Hearts did get through his defence.
Kearney said: "He is quality. He has been exceptional and his distribution is exceptional.
"He can kick it as far with his left as he can with his right. He can play outfield, he is technically that good and as a shot stopper and a keeper who wants to come off his line he had been brilliant."
