They currently sit fifth in the GUINNESS PRO12 table - although could be leap-frogged by Munster and Glasgow Warriors later this weekend - and are eight points behind fourth-placed Ulster with five games remaining.
That situation leads Solomons to believe that his troops face an uphill struggle to reach the play-offs for the first time since the structure was introduced in the 2009-10 campaign.
Against Connacht, Edinburgh found themselves 14-0 down at the break and 21-5 behind early in the second half before battling back to within a point.
But Eoin McKeon's try sealed the victory - and the bonus point - for the Galway-based side, leaving Solomons to bemoan his troops' lack of concentration at vital moments.
"I am very disappointed. In the first half, Connacht played really well and absolutely deserved their lead," said Solomons.
"In the second half, we got on top of them and had two defensive lapses that cost us 14 points. But for those lapses, we could have and should have won the game.
"We had a problem at the breakdown and we had to deal with that and I thought we sorted that out at half time.
"I thought the forwards did well considering that nine front-line guys are out of our pack and sometimes you are down to the number three in a position.
"It is damaging [to our top-four hopes], no question about it. We are now in a situation where we certainly cannot afford to lose a game at home and we need to pick up probably two wins in tough away games."
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Guinness PRO12 Edinburgh News
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