United have recovered from their wobbly start to start to go on a 12-match unbeaten run, but the Red Devils have drawn their last two Barclays Premier League matches 2-2 to leave them ninth in the table.
Spurs took the lead against David Moyes' men at White Hart Lane on Sunday when Kyle Walker scored from a free-kick, which was awarded when Jonny Evans fouled Paulinho on the edge of the box.
That came seven days after Chris Smalling fouled Craig Noone to give Cardiff the free-kick from which they scored their 90th-minute equaliser against the champions.
Welbeck was content to take a point from north London this weekend, but he knows their task would have been made easier had they not gifted Tottenham the chance to score their opener.
"We gave away too many free-kicks which put us under pressure, so if we can limit ourselves from doing that then I'm sure we will be a lot better in future games," the United striker told MUTV.
"Coming to White Hart Lane, we had the ability to come and win the game.
"That was on our mind but unfortunately we gave away two goals. Credit to us, we quickly got the goals back afterwards. We are a bit disappointed but we can be happy with a point at the moment."
Moyes knows this month will be key to United's chances of finishing inside the top four this season.
After home games against his old club Everton and Newcastle, the Scot has a favourable set of fixtures including games against Aston Villa, Hull, Stoke, West Ham and Norwich.
Given that the games are packed so tightly together, Moyes will have to rotate his squad, and, luckily for him, he looks set to have Welbeck to call upon.
A knee injury kept the 23-year-old out of action for club and country for two months, but he is nearing full fitness.
"I wanted to get the winner but it didn't come this time. I need a couple more games," said Welbeck, who was substituted in the second half.
Unfortunately, after 60 or 70 minutes, my legs were gone as it was my first game back after two months and I started cramping up.
"I have been out for two months and you need some games and more hard training sessions to get back into it."
Welbeck helped United get back into the game by winning a penalty in the second half following a foul by Hugo Lloris.
Tottenham manager Andre Villas-Boas accused Welbeck of dangling his trailing leg in a bid to win the spot-kick.
"I saw Wayne getting the ball on the left, he was cutting inside so I made a diagonal run in behind the defender," Welbeck explained.
"I was aware of the keeper coming out but I wanted to get the ball first. I touched the ball and he clipped the back of my legs and knocked me off balance."
United will be without Phil Jones when Everton come to Old Trafford on Wednesday because he picked up his fifth booking of the season on Sunday.