The Saints finished in the Europa League qualification spots during the 2014/15 campaign, and Romeu says that a repeat season should be on the cards.
The Spanish midfielder believes that Southampton have a lot of quality in their squad, and he has challenged them to compete for a European place again this time around.
"Our expectations have to be to finish in the same spot as last season," he said. "If we can improve that it would be amazing, but with the team we have we should think to get into the same position - not lower than that. We have a good enough team to be there."
Southampton started this season slowly, but they have started to click into gear of late and are now looking to be back to their best.
Ronald Koeman has made the south coast club one of the most dangerous teams in England, and their attacking threat was on full display in their latest outing.
Southampton beat Chelsea 3-1 at Stamford Bridge over the weekend, with their performance drawing a number of plaudits.
That win has put Southampton into ninth place in the Premier League table, meaning they still have work to do to meet Romeu's target, but they are unbeaten their last three matches and have been climbing the standings quickly.