The hosts agonisingly ran out of time, one wicket short of victory, as their new Test era began with a nerve-jangling stalemate in north west London. James Anderson's burst of three wickets for one run either side of tea helped keep the outcome in doubt to the very last ball, as the tourists clung on at 201 for nine in the notional pursuit of a ground-record 390.
"I can't praise the lads enough today," Cook said. "That was a flat wicket and we had to wait for the ball to reverse swing. It finally got dry enough and did and Jimmy bowled really well."
However, despite the efforts of England's pace attack, Cook acknowledged that his side might have profited from the inclusion of a frontline spinner as they adjust to life without Graeme Swann.
"Possibly," he admitted when asked if a spinner would have been useful. "The mainline spinner could have made a difference but with the players we have available for selection this is the way we have to go and that's what we have to accept and I can't praise the lads highly enough."
That praise was also given the England's batsmen, who ensured the game always remained competitive.
"The batting in the team, in both innings . . . we scored at more than four runs an over which gave us the opportunity to win the game," Cook said. "At the moment it's a bit disappointing that we couldn't get over the line."
Man of the match was Joe Root, for his first innings double hundred. The Yorkshire batsman believes that nobody now could accuse England of being boring. "It was exciting, wasn't it?" he admitted. "Twelve months ago when we were told we're playing dour cricket. I don't think anyone can say that now. We spoke long and hard about making big scores, individually and as a team, and that's a great start for the summer."
Of his own contribution he added: "It fills me with a lot of confidence. To set the game up is what you need to do and we did that. When you've got 500 on the board it gives you a good chance even on a flat wicket.
"It was disappointing to be left out [in Australia] but I wanted to prove a point early in the summer and hopefully I've done that.
"I hope I stay at 5, I enjoyed it this week and fingers crossed we can sort something out. Gary Ballance played with great skill, batting at three is testament to his character as well."
Sri Lanka captain Angelo Mathews was also impressed with England's seamers. "We didn't bat well especially after tea," he said. "You can't really relax and that's a good lesson learned with the attack they have got. They have got some really good bowlers."
England have announced an unchanged squad for the second Investec Test at Headingley, which starts on Friday.