Paulo Sergio hailed his side's belief after they battled back from behind to defeat St Johnstone 2-1 in the fifth round of the William Hill Scottish Cup.
Marius Zaliukas' winner three minutes before the end of extra-time earned Hearts a last-eight meeting at home to St Mirren Murray Davidson's goal after 83 minutes appeared to have the hosts on course for a place in the quarter-finals before Jamie Hamill netted an injury-time equaliser from the penalty spot.
"We always believed that something could happen even at 1-0 down - at that moment I didn't believe we deserved to be out of the cup," said Sergio. "We made changes to our style to avoid St Johnstone profiting as they had in our previous meetings. You shouldn't forget this team is playing nine games in four weeks and some of our players aren't so fresh just now."
Sergio also paid tribute to the endeavour of their opponents. The former Sporting boss has hit the headlines recently following a war of words with Kilmarnock manager Kenny Shiels, but was keen to praise Saints' determination over the two ties.
"I have to say a good word to all of the professionals and staff at St Johnstone as both games were very tight," added Sergio. "I am very, very happy because I think we deserved the win but it could have been Steve (Lomas) speaking after the game saying the same."
Lomas was gutted after referee Brian Winter awarded Hearts a last-gasp penalty.
Alan Maybury was adjudged to have fouled Suso Santana inside the area and Jamie Hamill stepped up to force extra-time at McDiarmid Park.
"I watched the DVD and feel it was a very, very soft penalty. I feel for my boys as I asked for a much improved display after Saturday and they gave it everything," said Lomas.
"Sometimes you need a bit of luck in the cup, I don't want to criticise the referee, but when you see the replay on television he sees Alan Maybury and falls into him.
"We asked for a performance and felt we got that, but no matter what you do, you need a bit of luck. Ten seconds before the end the referee gives a penalty, it's a massive call from him."