Former Liverpool midfielder Patrik Berger got the only goal at Fratton Park, but Houllier pointed to a string of second-half chances that could have turned the game on its head.
"The main difference between the two sides was the freshness," he told the Merseyside club's website.
"We've had players away in Turkey (with England) and other internationals plus the European (UEFA Cup) game in midweek (a 3-0 home win over Olimpija of Slovenia).
"I don't think we had enough liveliness about us and they (Portsmouth) defended well. I can't fault their attitude, they just didn't have the legs.
But he added: "I wasn't happy with our performance and we weren't our usual selves from an attacking point of view, but when you have chances and we had enough of them, you have to take them."
Liverpool, missing injured England striker Michael Owen, got a more frank assessment of their display by newly-appointed captain Steven Gerrard.
NO EXCUSES
"We can't look for excuses," he told Sky Sports.
"We weren't good enough today as a team. We've got to have a good look at ourselves when we get home and prepare for next week and hopefully put it right."
Liverpool, who are ninth in the table before eight more teams play on Sunday and Monday, are at home to Leeds United next weekend.
Portsmouth manager Harry Redknapp, whose team had lost their last three games after a promising start to the season, said: "We deserved to get the three points today and our overall performances (have) deserved at least 12 points.
"I think we could be sitting here with 17 or 18 points, we've played well enough."
Newcastle United manager Bobby Robson watched a battling performance from his side as striker Shola Ameobi secured a 1-0 north-east derby victory over Middlesbrough, their second straight league win after a disappointing run.
Paying tribute to his team's determination, Robson said: "I'm delighted. It was one of those 'over-my-dead-body' performances, with a lot of resolution in the team.
"We blocked shots, intercepted, headed balls out and the keeper made some good saves. It wasn't a pretty performance ...but three valuable points have jumped us up the league."
Newcastle rose from 18th to 11th in the table with the win.
Manchester City manager Kevin Keegan felt his side lacked urgency in a first half that saw them drawing 1-1 at the break, but they turned on the style in the second half to record a 6-2 rout of Bolton Wanderers at the City of Manchester stadium.
Keegan said he told his players at halftime: "'We're at home, let's get after them'. And when we went one or two goals up we were breathtaking. But you've got to earn that right."
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