Onuachu was forced off in the 52nd minute of Sunday's 3-2 defeat to Liverpool, having impressed supporters with his effort and trickery.
Lallana was taken off before half-time with an injury Martin feared was more serious, and the 36-year-old is set to be sidelined with it.
Saints visit Lallana's former club Brighton & Hove Albion on Friday knowing not even a win can take them off the bottom of the Premier League table.
Speaking ahead of the contest, Martin said: "Adam is out, which is a shame because I think he would have loved to have been back at a place he had a really good time.
Saints are set to be without midfielder Adam LallanaSaints are set to be without midfielder Adam Lallana (Image: Stuart Martin)
"Adam's out and Paul's being assessed, so fingers crossed that big Paul will come through all right. It's not a bad injury at all, which is good news for us.
"It's just a niggle so hopefully we can manage that and he can be involved. I think Adam's going to be a couple of weeks, so probably the next couple of games."
Martin added: "Paul did brilliantly and he seems to be fine, recovering quite nicely. We had it scanned straight away because it was a bit of a worry.
"He had a brilliant impact because he brings something completely different. He's had to work so hard to get used to what we want from him.
"With Paul, a lot of it was trying to get him to do a bit less and be really effective in what we were asking him to do and he's so willing to work and work hard and improve.
"He's been desperate to play so I'm pleased for him but now we need to try and get him on the pitch tomorrow if we can and if not as soon as we possibly can."