Sunderland dragged themselves back into the match within seconds through Fabio Borini's effort, but they were second-best for an hour.
However, the Saints failed to capitalise on the wealth of opportunities they created and they were made to pay with 19 minutes remaining when Adam Johnson smashed a stinging shot through keeper Artur Boruc's hands to snatch a point.
Pochettino said: "I am quite disappointed with a point. I think we actually deserved to win the game, but in the end we leave with one point and two injuries."
Lovren, who was hurt in a challenge by substitute Craig Gardner, and Ramirez, who was caught by Wes Brown, were carried from the pitch within seconds of each other and the initial signs were not good.
Pochettino said: "You could see that they were in a lot of pain. I saw them before going to hospital and both of them were in a lot of pain."
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