Gunners striker Robin van Persie scored twice, the second in added time, to snatch victory at Anfield in a game in which they had been outplayed by Liverpool for long periods.
In truth Arsenal could have been out of the game by half-time had goalkeeper Wojciech Szczesny not made a great double save to deny Dirk Kuyt from the penalty spot before Laurent Koscielny's own goal put the hosts in front.
Despite seeing a sixth penalty of the season squandered, Dalglish said: "If you want to gauge it on points then it is a big disappointment but if you want to gauge it on performance I think they were fantastic.
"I think we are competitive all right. I think those stats tell you we are attack-minded and can create chances and get penalties - the next bit is to be ugly and get a winning goal.
"There was always some scepticism to us winning a trophy (Carling Cup) the week before and how they would react and respond and I think they showed that with the way they played. To come away without three points is disappointing. The performance was outstanding - if we get a bit of luck it will make a difference to us."