Alonso said after playing his first exhibition with the team — as a second half substitute 5-1 win over Toronto FC — that he didn't think twice about making the North American trip.
"It's something that I wanted, to fly here to start getting to know my teammates," he said. "Now we'll have more time to spend together.
"It was great to play my first game with a new club, a new shirt, and new teammates."
Arjen Robben was on the scoresheet and said: "The quality of the players around you can only improve your game.
"At the moment there's a lot of competition, but it's a joy to play on this team.
"There are still some new players who played their first minutes today, but we have three or four more games, so we have to use all the time to start playing as a team.
"We just have to play a lot together and get used to each other, that's the most important thing."
NBA star Steve Nash conducted a post-game interview with Kaka, who also made his Real debut on the night, and said: "He's an idol to me, and it was special not only to see him, but that it was here in Canada. He's told me he only practised for a week, but who could tell?"