Chelsea took the lead through Sandro Tonali's deflected effort before Estevao Willian levelled with a header from Jamie Gittens' cross, but Kevin Danso's second-half red card for denying Joao Pedro a clear goalscoring chance left the Blues facing the closing stages a man down, and Richarlison eventually snatched a stoppage-time winner for Tottenham to complete the London derby double header down under.
Alonso was asked at length about Mudryk, whose doping ban was lifted this week, and did not hide his enthusiasm for having the winger available again.
"We are happy for him, especially for him. Probably we are not able to understand what we've been through in these moments. We want him to be a part of the team. He has the support of everyone," he said, confirming Mudryk would join up with the squad in Hong Kong for the next stage of pre-season.
Asked what the Ukrainian will bring to the side, Alonso reflected on watching him during his time at Shakhtar Donetsk: "I watched him at Shakhtar, the impact he had, how good he is in one-v-one situations. He can create a lot of situations on his own.
"He's a special player. But it will take time, for sure."
He added that patience would be essential given the length of Mudryk's absence: "It will take time but once things have changed, things will start moving. He wants to play football and be part of the team, it must have been really hard for him."
On team news, Alonso confirmed goalkeeper Mike Penders would also link up with the squad in Hong Kong, while fellow shot-stopper Robert Sanchez has picked up only a minor injury.
Reflecting on the defeat itself, Alonso was pragmatic rather than downbeat.
"It was an intense, competitive game. We wanted to win. For sure, to lose this, we don't like it but it's pre-season. We missed a few chances. First-half was even and in the second-half we were very close to score that goal. Great pre-season game but unlucky to concede a late goal," he said, adding when pushed on the performance: "Of course, in any game, you think you can do better — that's part of the process. This is normal that we're going through these moments."