They slipped to 17th in the table thanks to the defeat, but were much improved after the break, with Wojciech Szczesny producing a great save to deny Fraizer Campbell an equaliser with the score at 1-0.
"The score is not a fair reflection of the game, but I am not going to apologise for having a go," he said.
"That's what we did, and we certainly gave them some problems in the second half. The calmness on the ball in the second half makes me very proud of the players.
"We were playing against a team who have had a manager in situ for 17 years. Over that time he has had a lot of money to build a recruitment process to bring in top players like we have seen here.
"We were playing against the best and were certainly not out of our league."
Mackay also has no doubt Arsenal have what it takes to retain their position at the top of the pile.
He said: "They've got a very good chance, if they are sitting first today.
"They are in the last-16 in Europe as well. It speaks for itself, it's not rocket science."