The former England striker, signed as a free agent earlier this month, appeared as a last-minute substitute as the Potters held the Barclays Premier League champions to a 1-1 draw at the Britannia Stadium on Saturday.
Owen, 32, is hoping to resurrect his career after three injury-ravaged years at Manchester United, who released him at the end of last season.
Manager Tony Pulis does not yet think Owen is match-fit but he could come into contention for next week's trip to Chelsea.
Pulis said: "Michael has trained ever so well over the last couple of days. He is desperate to get going.
"But he needs a lot more football. He has done a lot of work by himself, fitness-wise, but playing games is a lot different from just running."
Pulis also gave a debut to new signing Steven Nzonzi while Charlie Adam was given his first start against City.
Now in their fifth season in the Premier League, the Potters are well established in the top flight and have ambitions to firmly implant themselves in the top half.
Pulis expects further improvement once all the squad have had significant time to train together, something the recent international break has prevented so far.
Pulis said: "I think we will get better. It will be nice to have them next week and work with them.
"We gave the ball away too many times but we've got better technical players in.
"We still need to retain our commitment and organisation but we have to retain the ball better when we do get it. There were times when we were giving it away too cheaply."
Pulis was unhappy with the defending which allowed the champions to fight back for a point - the fourth successive 1-1 stalemate between the clubs in this fixture - after Peter Crouch had struck a controversial opener.
Crouch netted from close range in the 15th minute but had clearly handled as he brought the ball under control. City debutant Javi Garcia levelled when allowed a free header at a set-piece 20 minutes later.
Pulis said: "I was really disappointed with the defending on that one. I thought we dropped too deep too early."
But commitment was clearly evident in the closing minutes as Asmir Begovic produced a fine save to deny Garcia a second and Ryan Shawcross cleared off the line from Edin Dzeko.
Midfielder Glenn Whelan told the club's website, www.stokecityfc.com: "Asmir put it on the post and it came back to him.
"I don't think he had too many saves to make so he will be happy with that.
"Then Ryan wasn't sleeping, he kept going right to the end. From where I was I thought it was in. He is a big lad and he got his big legs to it."
Whelan, who joined the club in their promotion-winning 2007-08 campaign, feels the signing of Owen is indicative of the great progress made under Pulis.
The Republic of Ireland international said: "It is massive. The manager said when we first came in it was a building process each year and each year we have found that.
"Obviously the club has pushed on - new training ground, signing big players.
"Hopefully the fans are grateful for that and will keep coming and cheering us on but it is up to us to give them something to cheer about.
"It is a great club to be around at the minute because there is a big buzz."