Hearts manager Craig Levein insisted his side should have taken all three points against Dundee United as they had to make do with a Betfred Cup bonus point by taking the penalty shootout after the game ended 1-1.
Irving was later red-carded for a handball on the edge of his own area with just six minutes remaining.
However, Levein felt the Gorgie outfit passed up more than enough gilt-edged opportunities to emerge with a victory.
He said: "I think we should have won in 90 minutes. I said to the players after the game I was quite happy with their performance.
"Experience tells me we'll get better. This was our first competitive match and I felt the pressure was on us; United could come and enjoy themselves.
"But I was really pleased with a lot of aspects in the match, particularly individual performances, and some of the combinations on the field worked really well. And for long, long spells we controlled the match.
"The little criticism was that with ruthlessness in front of goal we could have made the game much, much easier."
Dundee United boss Robbie Neilson saw his team fail from the penalty spot yet again after their promotion play-off failure against St Mirren back in May.
However, he felt there was plenty of reason for encouragement during the course of the 90 minutes.
He said: "To come down here against a top-six, probably top-four team, I'm happy.
"Any team, probably outside the Old Firm would take a point here, so I'm delighted with the players.
"I thought we proved to ourselves and everyone else we can play at this level."