Essex left-hander Cook was dropped by Imran Farhat on nought and 81, as well as surviving an easy return catch to leg-spinner Danish Kaneria on 45, while Durham all-rounder Collingwood escaped when on 79.
England finished the first day of a four-Test series on 309 for three, with Cook on 101 not out and Collingwood unbeaten on 109, the pair's fourth-wicket stand currently worth 221.
"It was not the best of days for Pakistan," admitted Waqar.
"If you look at the bowling performance, apart from the first spell, I thought the bowlers bowled extremely well," the Pakistan great, a thorn in England's side during the 1990s, added.
"They created the chances for the team but unfortunately the team could not hold on to the catches."
Waqar though had some sympathy for Pakistan's fielders, despite their failure to support an attack missing injured fast bowlers Shoaib Akhtar (ankle), Rana Naved-ul-Hasan (groin) and Mohammad Asif (elbow).
"The first time here at Lord's its not easy. There's a tense atmosphere and a different atmosphere from any other ground.
"It's beautiful here but it does tense you up - our bowlers were a little tense in the morning, that's why they bowled both sides of the pitch.
"But they got more relaxed and then bowled beautifully."
Waqar also blamed his side's missed chances on the poor visibility at Lord's, especially when conditions were cloudy.
"It's not easy to sight the ball here at Lord's," said Waqar. "It does get difficult when there are overcast conditions."
Waqar also bemoaned the absence of experienced slip fielder Younis Khan (knee) after Farhat dropped two catches at second slip, where the Pakistan vice-captain usually fields.
"He is probably the best slip fielder we've got," said Waqar.
"Imran Farhat has been a very regular slip fielder but when it's a bad day you drop one, then you drop everything.
"Younis is normally second and Imran Farhat is normally in third (slip)."
Meanwhile, Cook reflected on a memorable day for both himself and Collingwood. The pair were each scoring their first Test hundreds in England, and second overall, after they'd reached three figures for the first time against India at Nagpur in March - Cook's Test debut.
"It was a great moment to get a hundred at Lord's and one I'll never forget," said the 21-year-old Cook.
"I should have been caught on nought and a few other times but that's cricket -- when you get the luck you have to cash in and make the most of it."
Collingwood was equally delighted but warned England still had work to do if they were to press on to an impregnable total.
"It's just the start and we have to be as ruthless as we can."
Waqar added he was confident that Pakistan, ranked just above England at second in the International Cricket Council Test rankings, could bounce back on the second day and expose England's vulnerable lower order.
"Tomorrow (Friday) is a new day and we will take the new ball and try to bowl England out as soon as possible.
"England are in a very good position but the new ball will probably do something here. If we grab a couple of quick wickets we can probably come back into the game."