Saints looked in complete control after goals from Jay Rodriguez and Lovren inside the opening 31 minutes at St Mary's, but Fabio Borini quickly reduced Sunderland's arrears.
The Black Cats improved as the game went on and salvaged a point thanks to Adam Johnson's second-half strike, but Pochettino still felt Southampton deserved three points.
While he was satisfied with the performance, Pochettino's afternoon was soured in the closing stages when Ramirez and Lovren both had to be stretchered off after picking up injuries.
"I am worried for Dejan and Gaston - they've both gone to hospital and they are being analysed," said the Southampton boss.
"They both looked like really painful injuries. We just need to see what the assessment is."
Reflecting on the match, Pochettino added: "I'm not pleased with a point because I thought we were superior to Sunderland over the 90 minutes.
"It is a shame that on their first attack they scored.
"We got to 2-0 very quickly and thought we would be able to withstand their attacks.
"I'm happy with our overall game, not just the start of the match. We did well in light of a tough and difficult week."
It was a tough week for Southampton after the resignation of executive chairman Nicola Cortese, which fuelled talk about the long-term future of Pochettino.
The Argentine said: "I'm quite tired - exhausted, really. It has been a tough, emotional week with not a lot of sleep."