Chasing finals, the reigning A-League Men champions sit seventh on 29 points, two points behind sixth-placed Macarthur FC and one ahead of the eighth-placed Mariners.
But Marcus Younis (suspension) will miss Tuesday's game while Beach and Teague are unlikely to feature.
First-choice goalkeeper Beach missed City's 3-0 win over Western Sydney on Saturday night after tweaking his quad while away with the national team.
"He's really gonna be 50-50. He's got a slight strain in the quad,' Vidmar said.
"He tried to train yesterday but still felt it so I'd think something like that would be a seven-to-10 day injury, I would imagine - so I think Tuesday is going to be too short.
"So my view (is) and we've spoken with the medical department the other day to say 'I don't care if we don't see him until Friday if that gives him that extra four, five days where he can just let it settle and build up from there'.
"We won't make a decision until the end of next week."
Midfielder Teague, on loan from Belgian club Mechelen, started but was unable to overcome a lingering left knee issue and was substituted at halftime.
"He had some issues with his knee," Vidmar said.
"He had a cleanout during the course of the year when he was out at Mechelen and he's played quite a few games for us and had no problems, but now he's had some aggravation to it after the last game in Perth.
"We thought he was going to be OK and over the last few days he's joined the group again in training and has felt fine, but obviously ... towards the end of the first half he felt something again.
"So there is some aggravation there so we'll just have to wait and see how he pulls up but I think he was pretty sore at halftime."
Veteran Mathew Leckie is more likely to push to return against Wellington next Sunday.
The Wanderers hope to regain some big names for Saturday's derby against Sydney FC.
Brandon Borrello (groin), Ryan Fraser (achilles), Kosta Barbarouses (calf), Hiroshi Ibusuki (calf) and Jacob Farrell (groin) missed the City game, with Farrell's season likely over.
"We think they're one-weekers and obviously Kosta was someone who's been to international duty as well, coming back with the travel and it was probably just best for him not to travel this weekend," interim Gary van Egmond said.
"We'll assess that when we get back but we're pretty confident a number of those boys, apart from probably Jacob, we'll look to get back."
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