The goalkeeper saw his side slip further behind Manchester City in the the title race and they now trail by 12 points.
He believes that United must find a way to win those close games, particularly against big sides, to fulfil ambitions of silverware.
David de Gea kept a clean sheet against Chelsea but Manchester United drew a blank
De Gea told MUTV: ‘I think that the draw is fine, but if we want to do something good and we want to win trophies and win the league, we have to beat these teams.
‘We didn’t have many chances; we didn’t create too much. I think the last pass was what we missed.
‘We created good counterattacks, but at the end, the last pass wasn’t the best option, but at least we defended really well.
‘They [Chelsea] didn’t have many chances. They had a couple of chances, but the team was strong. We gave everything but it wasn’t enough, to be honest.’
De Gea thinks those are the kind of games United need to win to fulfil their ambitions
The next week is hugely significant for United if they are to have any chance of catching runaway leaders City.
Ole Gunnar Solskjaer’s side take on Crystal Palace on Wednesday before a massive top of the table encounter against City.
De Gea added: ‘Win the next game and then we play against them [City], so let’s see if we can beat them and we can be closer to them, because now they are winning games, they are playing well, and now the gap is bigger.
‘It’s not easy. But this is the Premier League; we want to give everything until the last game and fight to be as high as we can.’
United are getting ready for a big week with the Manchester derby at the end