After collecting four points from six on the road last week, Pools were hoping to cement their place in the Vanarama National League play-off mix on returning to home territory.
But they suffered their second 2-0 defeat at the Suit Direct Stadium in succession thanks to first-half goals from Joe Newton and Callum Maycock.
Askey told BBC Tees afterwards: “I think we played against a strong team. Obviously there is a reason why they have not been beaten all season and we were beaten by the better side on the night.
"I still think that the goals we conceded early on were avoidable.
"People not staying with their men. When people do not do that you are always going to be in trouble and it is not just this game, it has happened in numerous games.
"It is the easiest thing to do when you defend to get goalside. But for some it just does not click.”
Wing-back Newton opened the scoring in Tuesday night’s encounter after just eight minutes with midfielder Maycock slotting home in the 35th minute to double the advantage.
Striker Mani Dieseruvwe came close to reducing the arrears after the interval when his his 51st minute header well saved by Tommy Simkin.
Defender Zac Johnson, making his debut for Pools on loan from Sunderland, also came close to scoring when visiting substitute Josh Kelly cleared his strike off the line.
But Kelly twice threatened to increase Solihull’s lead as they withstood home pressure to counter attack effectively on the break.
Despite their defeat in front of 3,517 spectators, Pools remain in sixth place on 19 points ahead of the 3pm visit of Dorking Wanderers on Saturday.
The Surrey side will travel north in 14th place after a 1-0 victory at Ebbsfleet United.
Hartlepool: Jameson, Johnson, Onariase, Hendrie, Ferguson, Seaman, Crawford (Dolan 70), Finney, Grey (Aghatise 70), Umerah (Wreh 81), Dieseruvwe.
Subs not used: Dixon, Burton.
Booked: Onariase, Dieseruvwe,Johnson.
Solihull Moors: Simkin, Clarke, Newton, Morrison, Stearman, Craig, Osborne (Kelly 56), Maycock, Mafuta, Beck, Warburton.
Subs not used: Stevens, Hall, Brogan, Barratt.
Booked: Osborne, Craig, Kelly.
Ref: Paul Marsden (Lancashire).