The Welsh club have just one win from their last six matches in all competitions and crashed out of the FA Cup at the hands of Championship outfit Blackburn Rovers last weekend.
That defeat proved costly to Monk, who saw his side end the match with nine men following red cards for both Kyle Bartley and Gylfi Sigurdsson, both of whom will be suspended for Sunday's clash.
Sigurdsson's absence, in particular, will come as a blow to Monk - a former Southampton player - as he seeks an improvement on the performance that saw Swansea thumped 5-0 at home by Chelsea last time out in the league.
"We've had a dip in form in terms of the standards we've set ourselves this season," he said. "The last two games have been disappointing, but the players and I are fully aware of what we need to do.
"We need to fight to get back to the levels we set as soon as possible, grabbing that momentum to push us on in the second half of the season, which I am confident we will do.
"We knew it would be a difficult period because of the players missing, but I don't want to make excuses.
"It's about getting back to the basics of what we have done well this season, starting with this weekend's game against Southampton.
"We need to put on a performance on Sunday that will give us momentum."
Jack Cork is on the verge of completing a move from Southampton to Swansea, so will almost certainly not be involved for either side on Sunday, but Koeman will be boosted by the return of Maya Yoshida and Sadio Mane from international duty.
However, Southampton remain without the services of Victor Wanyama (hamstring), Morgan Schneiderlin (thigh) and Toby Alderweireld (hamstring).
"They are doing well," said Koeman at his pre-match news conference. "They are close to being back but not for this Sunday. Hopefully we will have these players available for next week."
Shane Long is out for around four weeks with a fractured rib.
In addition to suspended duo Sigurdsson and Bartley, Swansea are without Ki Sung-yueng, who remains at the Asian Cup, while Wayne Routledge (calf) is also sidelined.
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