West Ham have been struggling for form in recent weeks.
Sullivan said: “We have taken only three points from the last five games, but in all three draws we were so close to getting the win, so I can't be too downhearted.”
The Hammers picked up their third draw in the last five games this weekend, securing a 0-0 with Manchester United at Old Trafford.
Given their injury troubles, it was an impressive result for the Hammers, although they will rightfully feel they should have come away with all three points having had the best chances to score in the game.
This has been the story of West Ham’s recent form, having struggled to pick up points in recent weeks following the 2-1 victory over Chelsea in October.
They were comprehensively outplayed by Watford in a 2-0, managed a 1-1 draw at home to Everton, were thrashed at the hands of Spurs by a 4-1 scoreline, before recovering to again draw 1-1 at home to West Brom.
Three points from five games is not the form that Slaven Bilic will have wanted considering how well the East London side started the season, but the return of points should be considered impressive given their injury troubles.
Despite the results, Sullivan has admitted he is not too downhearted as the drawn games have been close fought encounters which the Hammers could have quite easily won.
There are fine lines between drawing and winning, but until the Hammers can start to change some of these draws to three points, they will struggle to replicate their early seen form and fight for European football.