The Eagles took a point away at Anfield thanks to an early goal from Wilfried Zaha.
Speaking to Sky Sports, Vieira said: "I am really pleased. It is not an easy place to come and we defended well as a team. We were prepared to suffer and did. In our counter-attacks we were good. We needed a big team performance and we had it tonight.
"When we won the ball Wilf ran in behind and the timing of his run was really good. Wilf is a goalscorer. Today he could score more than one.
"When you come to these places you accept you will go through difficult periods. It is about how you manage those and I think we did it will. The first 20 minutes, half an hour was tough but we were really composed, calm and disciplined. That helped us perform well.
"If we don't bring those ingredients, it is really difficult to get something from that game. We competed against them and worked hard. This is the minimum we can do. Then we need the organisation and discipline. We got the point and I am really pleased with that."