Danny Welbeck opened the scoring early in the Group A encounter at the Donbass Arena, before the home side's Brazilian attacker Taison grabbed a 76th-minute leveller as United clung on to secure a hard-fought point.
Although the Premier League champions were unable to claim all three points, Vidic was delighted with the way United responded to their disappointing home defeat against West Brom at the weekend.
|MANCHESTER UNITED LATEST
|10/1||Man Utd are 10/1 with William Hill to beat Sunderland 3-0
"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."
Vidic does not believe United have played their best football yet, and is keen to use the result against Shakhtar as a springboard for a good performance in their next league outing against Sunderland.
"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," continued the 31-year-old.
"We know we have not played at our best yet, but we still have time to improve and the next game is really important.
"We came to win, we wanted three points but we have to accept as well they were a good team.
"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."