Danny Welbeck's goal gave Davis Moyes' side the lead in the first-half, but after the hosts equalised through Taison the Reds held out for a hard-earned point, something no English side has done in a Champions League tie in the Donbass Arena.
Vidic was particularly pleased with the reaction to last Saturday's disappointing Barclays Premier League defeat to West Brom.
"The most important thing is I saw improvement," he told MUTV. "I saw solidity, I saw a reaction from the last game. We were hard to beat in all positions, not just at the back, but in midfield and wide, and that's the way we have to play. We have to work hard, play as a team and hopefully goals will come.
"We improved, we didn't let them have many chances to run at our defence. Our team worked really hard but there is still room to improve, and that's a good thing. We know we have not played at our best yet, but we still have time to improve and the next game is really important."
Shakhtar's comeback took some of the gloss off a solid United performance, but Vidic saw enough in the display to be encouraged for the games to come.
"We came to win, we wanted three points but we have to accept as well they were a good team," the Serb added. "They have quality players and it's hard to play away in the Champions League, but we had some improvement on the last game. That's encouraging and we showed character from what happened in the last game, and hopefully we can improve against Sunderland."