The punishment was imposed following a disciplinary hearing at Hampden on Monday, where Hearts were represented by owner Ann Budge, after the ineligible Andy Irving played in last Wednesday’s 2-1 Group C victory over Cove Rangers.
The midfielder came on as a 65th minute substitute, when Hearts were winning two-nil, but the Edinburgh club admitted a day later that the 18-year-old’s official registration expired on June 9 because his contract extension was not properly submitted to the Scottish FA in January.
The sanctions, which include a £10,000 fine - £8,000 of which is suspended until the end of next season - leaves Hearts on three points, two adrift of Inverness Caledonian Thistle and Cowdenbeath, whom they host this evening.
Levein, whose side picked up a bonus point with a penalty shoot-out win over Raith Rovers on Saturday, said: “We’re satisfied with the outcome of the hearing.
“Every case needs to be judged on its merits and that’s what the panel did; they considered all of the arguments before making their decision.
“I put Andy on the pitch as a young boy just to get some experience. We were winning 2-0 when he went on and we ended up winning 2-1 so we got no competitive advantage from it whatsoever.
“We can now focus fully on our match against Cowdenbeath at Tynecastle, knowing exactly what we have to do to get out of the group.
“Our aim is to progress in this competition and we’ll be going all out to do just that.”
Hearts wrap up the section with a visit of Inverness on Sunday but their hopes of progressing to the second round have been dealt a significant blow.
The eight group winners progress to the knock-out stages along with the four best runners-up.
As things stands, the teams currently occupying second place in all the other sections have better points tallies that Hearts, albeit Annan have played one more game in Group F.
The SPFL statement read: “At a disciplinary hearing, a sub-committee of the SPFL board charged Heart of Midlothian Football Club with playing an ineligible player (Andrew Irving) in their Betfred Cup group stage match against Cove Rangers FC on 18 July 2018.
“Heart of Midlothian admitted breaching SPFL rules and were deducted two points from their Betfred Cup first round group stage tally.
“The club were also fined £10,000 (of which £8,000 was suspended until the end of season 2019/20).”