The Toffees were second best for much of the Europa League Group H clash at the Kuban Stadium.
But they emerged with a point after veteran striker Samuel Eto’o — the ex-Anzhi Makhachkala player, back on Russian soil — notched a late equaliser.
Eto’o stabbed in Leighton Baines’s cross in the 82nd minute to cancel out Ari’s 43rd-minute goal for the hosts.
Having seen his team achieve what he described as an “incredible result”, Martinez said: “Today gave us a lot of experience. It has been a very good lesson for us. I think anything you can get away from home is a positive.
“I thought Krasnodar adapted well in the first half, better than us, and probably we then finished stronger.
“Maybe a draw is a fair result, but Krasnodar did have a lot of chances they couldn’t take and it could have been a different story.”
In the other Group H game, Wolfsburg were frustrated by an inspired display from Lille goalkeeper Vincent Enyeama and some awful finishing as they were held to a 1-1 draw in Germany.
The Bundesliga side, looking to bounce back from a 4-1 mauling at Everton, dominated play and carved out a host of chances only to find Enyeama in imperious form.
They were made to pay for those misses when Ricardo Rodriguez, who had scored an own-goal at Goodison Park, handled the ball in the area with 15 minutes left and Belgium striker Divock Origi scored from the spot.
Kevin De Bruyne equalised with a stunning 25-yard volley with eight minutes remaining, but this was most definitely two points dropped for the hosts.
A calamitous display from Vlad Chiriches eventually undid all of goalkeeper Hugo Lloris’s good work as a last-gasp penalty earned Besiktas a hard-fought 1-1 draw at Tottenham.
Spurs came into the match buoyed by Saturday’s draw at bitter rivals Arsenal — a team Slaven Bilic’s side pushed close in this season’s Champions League play-offs.
Defeat to the Gunners saw the Turkish outfit drop into the Europa League, where they looked set to suffer more north London frustration until Demba Ba’s last-gasp penalty cancelled out Harry Kane’s 20-yard strike.
The only survivor from the north London derby team, Lloris was involved from the outset and produced a wonderful fingertip save to push an early Ba effort on to the woodwork and then made three more top-class saves after Kane’s 27th-minute opener.
However, Ba finally got the better of him from 12 yards after Chiriches failed to clear a bouncing ball and then compounded his error by poking it away with his hand in the ensuing panic.
Lloris said: “It’s football. Sometimes you don’t play a good game and you have to know how to win. Today we were close but conceded a penalty. It’s a good thing to learn.”
An early Kris Commons goal gave Celtic a hard-fought 1-0 win over Dinamo Zagreb in their Europa League Group D clash at Parkhead.
The 31-year-old combined with Anthony Stokes in the sixth minute to fire past Zagreb keeper Eduardo but the classy Croatian side came back and before the break their Portuguese forward Wilson Eduardo hit the bar.
The home side were on the back foot for long spells with goalkeeper Craig Gordon having another impressive night in the Hoops goal making several crucial saves but in the end Ronny Deila’s side held out for the victory.
In Group G, it needed a stoppage-time equaliser from substitute Stephane Mbia to earn Europa League holders Sevilla a 2-2 draw at Rijeka, while in Rotterdam, Elvis Manu hit a late winner as Feyenoord beat Standard Liege 2-1.