Title-chasing CSKA were beaten by Russian Premier League leaders Zenit on Sunday and suffered another damaging loss in midweek as they slipped to third.
Georgi Milanov had cancelled out Alexei Ionov's ninth-minute opener only for Balazs Dzsudzsak to score the winner inside half an hour as Dinamo moved within four points of their near neighbours.
Despite back-to-back defeats at the business end of the campaign, Slutskiy maintained fine margins cost his side.
"We showed good quality. We conceded an early goal, but managed to equalise soon after," he told reporters.
"Unfortunately, Dinamo scored very easy, while we couldn't convert our chances. Matches like this one are usually decided by small margins. Those margins didn't work for us."
With CSKA stalling again, Krasnodar's 2-1 win over Rubin Kazan on Tuesday takes them second behind Zenit - Mauricio Pereyra at the double following Vladimir Dyadyun's opener.
Andre Villas-Boas' Zenit took another step towards the title as they fought back from a goal down to see off Terek Grozny 2-1.
Oleg Shatov and Salomon Rondon were on the scoresheet as the champions-in-waiting extended their unbeaten league run to seven matches.
At the bottom, Amkar Perm's survival hopes were dealt another below as they were beaten 1-0 by Mordovia Saransk.
Yannick Djalo's early penalty did the damage before the visitors were reduced to 10 men as Dmitri Belorukov was shown a second yellow card seven minutes from time.
Dmitri Smirnov's 91st-minute goal secured a 1-0 win for second-bottom Arsenal Tula against Spartak Moscow, and fellow strugglers Rostov beat Ufa 2-0 to leapfrog their opponents in the table.
Ural were another side near the bottom of the standings to triumph, winning 2-0 at Kuban Krasnodar, while Lokomotiv Moscow won by the same scoreline against Torpedo Moscow - Manuel Fernandes scoring twice prior to Vladimir Rykov's red card.
