Strachan commended his side for their effort and just thought that Arsenal's class was the difference between the two sides.
"We honestly thought we could have won, but you have to remember they have more experience, are more skilful, quicker and stronger," said Strachan.
"To be winners in football and life you have to take disappointment, so next time you know what to do.
"We do believe we could have won the game, we knew that they would make twice as many chances - as they do against every team, but we had chances and did not take them
"We stood up and did well, you can't enjoy a day like this - but I was very proud of them, if you don't win you must compete and we did compete.
"This defeat will stick with us, it is a horrible season and we must use this and go on.
"The way we competed was excellent, we had a lot things going right
"It is a season of achievement, we have got higher place in the league, higher points, full attendances and we are in Europe - so what more could we want."
Strachan also paid tribute to youngster Chris Barid, who had an outstanding game at right back in only his second ever start.
"He had a fantastic game," said Strachan ."
"He did well at City on his debut down that side and we needed more strength as they can expose you there and he and Telfer were great."
