Spurs were second best for long periods at Wembley as Georginio Wijnaldum and Roberto Firmino scored either side of half-time, but a goal from substitute Erik Lamela set up a grandstand finale.
And they might have had the chance to snatch a point from the spot, only for referee Michael Oliver to remain unmoved when Sadio Mane clumsily challenged Son Heung-min.
"Of course, I think they were better. We competed, we were close and the last action was crazy because it was a penalty," Pochettino told Sky Sports .
"We should be talking in a different way, but Liverpool were better.
"I am disappointed with the result. We need to keep working and improving. It's only early in the season, we need to improve a lot."
Yet Pochettino insisted flaws were also on show at Old Trafford and believes the heavy workload a number of his first-team stars undertook during the World Cup have taken a toll.
"It is easy to criticise the performance because we lost the game and conceded many chances, but the circumstances were the same when we beat Manchester United," he said.
"It is a lot to analyse and try to fix. I think we are far way in terms of performance.
"It is early in the season. It is a moment to be calm and clear with the assessment, help the team to improve and be more consistent in our performance."
Pochettino added: "I am not a person who suffers too much. I try to find the solution. Don't worry for me – we need to be worried for the real things. I am so good, I am so happy.
"We started the season with good results, but we knew the circumstances and the reality after the World Cup were completely different.
"I was relaxed and not worried and today I am relaxed and not worried. My faith in this group of players is 200 per cent, not 100 per cent."