The Gunners took the lead through Bruce's former player Nicklas Bendtner after just two minutes then conceded again to Mesut Ozil within moments of the opening to the second half.
"It gives you a really difficult evening," said Bruce. "You want to give yourselves a foothold and we're 1-0 down after a minute. Then we did exactly the same at the start of the second half.
"It would be nice to keep it at 1-0 and exert a bit of pressure but overall they were better than us and they are very difficult to contain. They were very, very good on the night.
"When they get their tails up and they score early, they are a team to match anybody. It was a difficult evening to say the least."
Even though his side left the Emirates with nothing, Bruce was still pleased with the resilience shown by his players.
"You need your team to stick in with it and they certainly stuck at it. Thankfully they have got a bit of pride about them. If they hadn't it could have been a really horrible evening."
Bruce also had time to reflect on the contribution of Bendtner. The Tigers boss was the Dane's manager when the striker had loan spells at Birmingham and then at Sunderland.
"He is a good football player for the size of him. I hope that sooner or later he really knuckles down and really makes a go of his career because he's a very, very good player, but the mentality of Nicklas is always what everybody questions," said Bruce.
"He's a big, strong, powerful centre-forward who's good in the air and has good feet for the size of him. He's got the lot really, if he wants it - but there's always a 'but'."
Bruce added: "Did we try to sign him in the summer? We were having a look, but the level of salary was always going to be a problem for us.
"Nicklas is a good boy, he has always done well for me and it was Sod's Law he would do that against us today."