Hodgson told Sky Sports: "They have got a lot of quality. At 1-1 we were playing well and I thought we were on the front foot.
"Not comfortable but holding our end up. With the second goal knew then it would be an uphill task.
"But credit to the players. We did not capitulate after the third goal. Our second goal was scant reward for our play. It was a good performance form Arsenal. We were beaten by the better team in the end.
"When they were pushing us back with wide players we were not getting out quick enough following clearances. They sustained their attacks. In the second half we got closer to players in midfield. It was a good performance in terms of aggression and determination. If you give their three midfield players time they don't give it back.
"There are no positives in defeat as such. It is good we didn't get beat by more goals. Goal difference is important.
"We showed we are a good team and we have quality players in our team. For us it is a question of keeping fighting. Even at 3-1 down to a team of this quality there was no resignation or sign of not doing the right things. Had the game been five or six minutes longer maybe we could have got something."