The 23-year-old set die Roten on their way to a comfortable 3-1 win over the Gunners, and declared that they had outplayed one of the continent's best teams in the process.
"During a long part of the game we showed an outstanding performance against a top European team. We played very confidently," Kroos told reporters after the game.
"There was just one short phase where Arsenal were better and had some chances, but you cannot always prevent that."
Bastian Schweinsteiger echoed the statements of his team-mate but refused to rule out the Gunners turning the tables in the return fixture.
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"For me, the third goal was very important, but it is too early to write Arsenal off," he said.
"In the first 30 minutes we did very well. We passed the ball and chased the opponents across the pitch. We were very efficient."
The Bayern midfielder picked up a yellow card that will rule him out of the game at the Allianz Arena, and said he was not sure it was deserved.
"Of course I did not want that [to miss the second leg]. I did not throw the ball away very far and it was not a foul by Thomas Muller before. There were many yellow cards tonight, there should have not been [as many] yellow cards."
The current Bundesliga leaders will welcome Arsenal to the Allianz Arena on March 13 for the second leg.