The 32-year-old saw Clint Dempsey score in the 93rd minute to share the spoils with Sir Alex Ferguson's team, and says his side earned their point against the league leaders
Despite snowy conditions in north London the game went ahead, and Dempsey netted in the 93rd minute to ruin United's hopes of going seven points clear of Manchester City after Robin van Persie's first-half header.
Parker feels Spurs can now build on this performance and work towards qualifying for the Champions League after they strengthened their grip on fourth place.
"We came here and really if there was ever a time we were planning on getting a result it was today," he told Sky Sports.
"I don't think Man United were probably at their best and we put a lot of pressure on them in the second half and we got the deserved goal - we deserved to get a point out of that game, definitely.
"I think we've shown a real resilience, we've had a good first half to the season. We need to now go and push on, keep getting points, keep as tight as we can.
"Our objective is fourth but if we can improve on that and get better than that then so be it."
Parker was making his first league start of the season after a long-term heel injury and admitted that the winter conditions had made the match difficult.
"I was obviously pleased to be back out there, it's been a long while since I've been out there so it was very pleasing," he continued. "It was a tough game and I thoroughly enjoyed it and I hope I stay find and can carry on.
"Vision-wise the snow was coming in our faces so it was quite difficult, especially the first half with the wind, but it was the same for both teams."
Dempsey has now scored twice against United this season having previously failed to find the target against Sir Alex Ferguson's team and was hopeful of Spurs' chances of remaining in the top four.
"This season, before that I'd never scored against them, so it's good to help the team and get results, so things are good," he commented.
"We believe in ourselves and we've been given good results and been on a good run of form. I think we have the quality in ourselves that we can get results that will keep us in the top four."
The American forward also expressed astonishment at David de Gea's superb reaction stop to deny him in the second half.
"Oh man, he's a top goalkeeper and he made good saves but I couldn't believe he saved that; I though it was going in and I was going to celebrate, what a great save," Dempsey remarked.