Phillips is set to line up for the reigning RBS 6 Nations champions against South Africa on November 9, which would be his first appearance since being sacked by French club Bayonne.
Bayonne confirmed on Tuesday - 24 hours after Phillips announced it - that his contract had been terminated.
He allegedly turned up drunk for a player video analysis session at the Top 14 club earlier this month.
Phillips, though, intends to issue legal proceedings against Bayonne.
Phillips trained with Wales in a public session at the Millennium Stadium on Tuesday - it was watched by a crowd of just under 10,000 - and he looks set to start the autumn series opener against the Springboks.
"The players have been quite respectful of Mike and not really asked him about what happened," Warburton said.
"I am sure he is sick of answering all the questions, and we have kind of left him alone.
"But whenever he has been in a Welsh shirt he has always played great, so I am sure he will put things behind him and perform this autumn."
Warburton's public backing for his fellow British and Irish Lion follows that of Wales coach Warren Gatland, with the 77 times-capped scrum-half remaining a pivotal player in a squad preparing to face the Springboks, Argentina, Tonga and Australia next month.
Phillips claims he learned of his dismissal from an interview in a French newspaper on Monday morning, when Bayonne chairman Alain Afflelou described Phillips' alleged behaviour as "treason".
But there were no outward signs of his Bayonne issues as Phillips played a full part in an hour-long session conducted by Gatland and coaching assistants Rob Howley, Shaun Edwards, Robin McBryde and Neil Jenkins.
Warburton, meanwhile, has made an immediate statement of intent as Wales look to start redressing the balance in terms of a miserable record against major southern hemisphere opposition.
"Getting that win against a southern hemisphere side is something we have been looking forward to for such a long time," he added.
"We have got to the stage now where we have done well in the northern hemisphere, but I always look at the England team of 2003 that managed to play the Tri-Nations sides and beat them all.
"As a group of players, that has to be the next step for us. We keep doing well in the Six Nations, and that is your bread and butter.
"But it is getting to the stage now where we have to perform in the autumn and start taking the southern hemisphere scalps."