Jenna Schillaci scored both goals in the 3-2 defeat in the FA Women's Premier League - the team's sixth loss in the FAWPL.
However, the pre-season target of finishing higher than last term's best-ever fifth place is still very much on with the team also alive in all four cup competitions - the SSE Women's FA Cup, League Cup, Ryman Cup and London FA Capital Cup.
"The players are determined to succeed and we just have to stay positive and believe in ourselves," said manager Karen.
"I feel we're capable of beating anyone but we're finding that we're just falling short in the minor details against the better teams and getting punished for it."
That was very much the case again against Pompey on Sunday, where Schillaci's long-range free-kick opened the scoring and Spurs had the chances to build on 1-0 before the home team turned the game around.
Katie O'Leary slid a one-on-one chance just wide and Bianca Baptiste fired narrowly over before Ini Umotong powered through to level five minutes from half-time.
Lucia Leon and Lucy Loomes both went close from distance but quickfire goals from Lucy Quinn and an unlucky own goal from Wendy Martin and Spurs were suddenly 3-1 down with five minutes to go.
Schillaci curled a corner straight home for 3-2 in the second minute of added time but it stayed at 3-2.
"We had chances at 1-0, the game could have gone either way at 1-1 but the own goal was the key moment, it was a fluke goal and no-one could do a thing about it," added Karen.
"Full credit to the the players, they kept going and pulled a goal back late on but there was no time for an equaliser."
Spurs face table-topping Brighton in the FAWPL on Sunday (2pm).
Spurs Ladies v Portsmouth: Chloe Morgan, Sophie McLean, Leah Rawle, Jenna Schillaci, Lucia Leon, Shannon Moloney, Wendy Martin, Ri Soobadoo, Lucy Loomes, Katie O'Leary, Bianca Baptiste.