The Buddies sit second bottom of the table after Tuesday night's 1-0 home loss to St Johnstone made it seven defeats in eight games.
Danny Lennon's men struggled to impose themselves on St Johnstone and they are now in danger of losing touch with their three other rivals for the relegation play-off spot.
With the pressure mounting, Thompson admits the Buddies are failing in all the crucial areas.
Asked if a squad containing internationals such as Marian Kello, Eric Djemba-Djemba, Gary Teale and himself was too good to be relegated, he said: "No-one is ever too good to go down. It's fair to say we are underachieving and that results haven't been good enough.
"The league table doesn't lie and if you look at our goal difference, we've got the second worst figure in the table. We haven't been scoring enough goals collectively and we are conceding too many."
Kilmarnock and Ross County are both now three points better off, while 10th-placed Partick are two in front ahead of Wednesday night's Firhill clash with champions-elect Celtic.
St Mirren looked confident in the opening stages against their Perth guests on Tuesday but the longer they went without scoring, the quicker their belief evaporated.
And Thompson says his team-mates must show more resolve if they are to prolong their eight-year stay in the top flight.
"The first four or five minutes we were reasonably bright but after that I don't think we were anywhere near the tempo we have been playing at over the last two or three matches," said Saints' 14-goal top-scorer Thompson.
"We were hesitant on the ball and possibly looked a wee bit nervy.
"With the position we are in, that is when you need to stand up and be counted and take the ball. But we were a bit quick to get rid of it against St Johnstone. It's fair to say we were poor.
"Do I think our league position is getting to the players? No, not yet. But I think we need to show a bit more character and a bit more belief, because we are in this position now and it's time to roll the sleeves up and there is no hiding place in these games."